{ "cells": [ { "cell_type": "markdown", "id": "3bbe8002-bdf3-490c-bde0-80dd3713a3d0", "metadata": {}, "source": [ "## `A <-> B` , downregulated by the \"shunt\" (coupled reaction) `A <-> S`\n", "### _Kinetic_ advantage (downregulation in early phase) vs. _Thermodynamic_ advantage (long-term downregulation) \n", "\n", "**[Scenario 1](#down_regulate_1_scenario_1)** : No downregulation on `A <-> B `\n", "\n", "**[Scenario 2](#down_regulate_1_scenario_2)** : The shunt (`A <-> S`) has a *kinetic* advantage but *thermodynamic* DIS-advantage compared to `A <-> B ` \n", "(i.e. `A <-> S` is fast, but energetically unfavored) \n", "\n", "**[Scenario 3](#down_regulate_1_scenario_3)** : The shunt (`A <-> S`) is has a *kinetic* DIS-advantage but a *thermodynamic* advantage compared to `A <-> B` \n", "(i.e. `A <-> S` is slow, but energetically favored) \n", "\n", "All reactions 1st order, mostly forward. Taken to equilibrium.\n", "\n", "LAST REVISED: May 5, 2024" ] }, { "cell_type": "markdown", "id": "61171e99-518e-4019-a731-be7437e95dfd", "metadata": {}, "source": [ "## Bathtub analogy:\n", "A is initially full, while B and S are empty. \n", "If the \"shunt\" S is present, scenario 2 corresponds to a large pipe and a small elevation change... \n", "while scenario 3 corresponds to a narrow pipe and a large elevation change." ] }, { "cell_type": "markdown", "id": "832afe37-f169-41c8-a719-e739336bc5cf", "metadata": {}, "source": [ "![Downregulated by shunt](../../docs/down_regulate_1.png)" ] }, { "cell_type": "code", "execution_count": 1, "id": "c4231a63-e456-48e9-bf4f-d074bbd3490a", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Added 'D:\\Docs\\- MY CODE\\BioSimulations\\life123-Win7' to sys.path\n" ] } ], "source": [ "import set_path # Importing this module will add the project's home directory to sys.path" ] }, { "cell_type": "code", "execution_count": 2, "id": "64933384", "metadata": { "tags": [] }, "outputs": [], "source": [ "from experiments.get_notebook_info import get_notebook_basename\n", "\n", "from src.modules.chemicals.chem_data import ChemData as chem\n", "from src.modules.reactions.reaction_dynamics import ReactionDynamics\n", "\n", "import plotly.express as px\n", "from src.modules.visualization.graphic_log import GraphicLog" ] }, { "cell_type": "code", "execution_count": 3, "id": "83c3cc5f-de21-4f66-9988-2806fbf0666d", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-> Output will be LOGGED into the file 'down_regulate_1.log.htm'\n" ] } ], "source": [ "# Initialize the HTML logging (for the graphics)\n", "log_file = get_notebook_basename() + \".log.htm\" # Use the notebook base filename for the log file\n", "\n", "# Set up the use of some specified graphic (Vue) components\n", "GraphicLog.config(filename=log_file,\n", " components=[\"vue_cytoscape_2\"],\n", " extra_js=\"https://cdnjs.cloudflare.com/ajax/libs/cytoscape/3.21.2/cytoscape.umd.js\")" ] }, { "cell_type": "code", "execution_count": null, "id": "001bc666-f2ef-40a3-b46f-30b087ea33da", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "35b5ef15-69da-4fc9-b1e9-fd34a9bafb99", "metadata": {}, "source": [ "# Scenario 1: A <-> B in the absence of the 2nd reaction" ] }, { "cell_type": "markdown", "id": "9329208b-070f-4902-8f37-0f11ddf75ed6", "metadata": {}, "source": [ "### Initialize the System\n", "Specify the chemicals and the reaction" ] }, { "cell_type": "code", "execution_count": 4, "id": "57d8431c-d6d0-462c-af78-e64eeb220e2e", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 1 (at temp. 25 C)\n", "0: A <-> B (kF = 30 / kR = 5 / delta_G = -4,441.7 / K = 6) | 1st order in all reactants & products\n", "Set of chemicals involved in the above reactions: {'B', 'A'}\n" ] } ], "source": [ "# Specify the chemicals\n", "chem_data = chem(names=[\"A\", \"B\"])\n", "\n", "# Reaction A <-> B\n", "chem_data.add_reaction(reactants=[\"A\"], products=[\"B\"],\n", " forward_rate=30., reverse_rate=5.)\n", "\n", "chem_data.describe_reactions()" ] }, { "cell_type": "markdown", "id": "f5eabdf2-0e6b-4141-a886-10974dfc6c3a", "metadata": {}, "source": [ "### Set the initial concentrations of all the chemicals, in their index order" ] }, { "cell_type": "code", "execution_count": 5, "id": "67a0375f-a14f-4cbe-965b-81d4c841aeab", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "2 species:\n", " Species 0 (A). Conc: 50.0\n", " Species 1 (B). Conc: 0.0\n", "Set of chemicals involved in reactions: {'B', 'A'}\n" ] } ], "source": [ "dynamics = ReactionDynamics(chem_data=chem_data)\n", "dynamics.set_conc([50., 0.], snapshot=True)\n", "dynamics.describe_state()" ] }, { "cell_type": "markdown", "id": "72a2148e-1aae-4ed7-bab3-5781b3a80fb0", "metadata": {}, "source": [ "### Run the reaction" ] }, { "cell_type": "code", "execution_count": 6, "id": "89f23b49-2840-4517-a275-b6a4f97898af", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "49 total step(s) taken\n" ] } ], "source": [ "dynamics.set_diagnostics() # To save diagnostic information about the call to single_compartment_react()\n", "\n", "# All of these settings are currently close to the default values... but subject to change; set for repeatability\n", "dynamics.set_thresholds(norm=\"norm_A\", low=0.5, high=1.0, abort=1.44)\n", "dynamics.set_thresholds(norm=\"norm_B\", low=0.08, high=0.5, abort=1.5)\n", "dynamics.set_step_factors(upshift=1.5, downshift=0.5, abort=0.5)\n", "dynamics.set_error_step_factor(0.5)\n", "\n", "# The changes of concentrations vary very rapidly early on; automated variable timesteps will take care of that\n", "dynamics.single_compartment_react(initial_step=0.001, reaction_duration=0.3,\n", " snapshots={\"initial_caption\": \"1st reaction step\",\n", " \"final_caption\": \"last reaction step\"},\n", " variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "code", "execution_count": 7, "id": "80fbaee3-bd6f-4197-9270-23374d46a4a7", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABcaption
00.00000050.0000000.000000Initial state
10.00100048.5000001.5000001st reaction step
20.00150047.7762502.223750
30.00200047.0651662.934834
40.00250046.3665253.633475
50.00300045.6801114.319889
60.00350045.0057094.994291
70.00400044.3431095.656891
80.00450043.6921056.307895
90.00500043.0524936.947507
100.00550042.4240747.575926
110.00600041.8066538.193347
120.00650041.2000378.799963
130.00725040.3060369.693964
140.00800039.43550210.564498
150.00875038.58782011.412180
160.00950037.76239012.237610
170.01062536.55674613.443254
180.01175035.39857414.601426
190.01287534.28600515.713995
200.01400033.21724416.782756
210.01512532.19056517.809435
220.01625031.20431118.795689
230.01793829.78318220.216818
240.01878129.11458520.885415
250.02004728.14130621.858694
260.02194526.74605723.253943
270.02384425.44351624.556484
280.02574224.22752325.772477
290.02764123.09232726.907673
300.02953922.03256027.967440
310.03143821.04320928.956791
320.03428519.65778930.342211
330.03713318.41045131.589549
340.03998017.28743332.712567
350.04282816.27634433.723656
360.04567615.36602834.633972
370.04994714.13664835.863352
380.05421913.09106236.908938
390.05849012.20179437.798206
400.06489711.06731338.932687
410.07130510.18724239.812758
420.0809169.16317440.836826
430.0905268.48358141.516419
440.1049437.80709342.192907
450.1265677.30436442.695636
460.1590047.12100842.878992
470.2076587.15821542.841785
480.2806417.11898542.881015
490.3901147.21045242.789548last reaction step
\n", "
" ], "text/plain": [ " SYSTEM TIME A B caption\n", "0 0.000000 50.000000 0.000000 Initial state\n", "1 0.001000 48.500000 1.500000 1st reaction step\n", "2 0.001500 47.776250 2.223750 \n", "3 0.002000 47.065166 2.934834 \n", "4 0.002500 46.366525 3.633475 \n", "5 0.003000 45.680111 4.319889 \n", "6 0.003500 45.005709 4.994291 \n", "7 0.004000 44.343109 5.656891 \n", "8 0.004500 43.692105 6.307895 \n", "9 0.005000 43.052493 6.947507 \n", "10 0.005500 42.424074 7.575926 \n", "11 0.006000 41.806653 8.193347 \n", "12 0.006500 41.200037 8.799963 \n", "13 0.007250 40.306036 9.693964 \n", "14 0.008000 39.435502 10.564498 \n", "15 0.008750 38.587820 11.412180 \n", "16 0.009500 37.762390 12.237610 \n", "17 0.010625 36.556746 13.443254 \n", "18 0.011750 35.398574 14.601426 \n", "19 0.012875 34.286005 15.713995 \n", "20 0.014000 33.217244 16.782756 \n", "21 0.015125 32.190565 17.809435 \n", "22 0.016250 31.204311 18.795689 \n", "23 0.017938 29.783182 20.216818 \n", "24 0.018781 29.114585 20.885415 \n", "25 0.020047 28.141306 21.858694 \n", "26 0.021945 26.746057 23.253943 \n", "27 0.023844 25.443516 24.556484 \n", "28 0.025742 24.227523 25.772477 \n", "29 0.027641 23.092327 26.907673 \n", "30 0.029539 22.032560 27.967440 \n", "31 0.031438 21.043209 28.956791 \n", "32 0.034285 19.657789 30.342211 \n", "33 0.037133 18.410451 31.589549 \n", "34 0.039980 17.287433 32.712567 \n", "35 0.042828 16.276344 33.723656 \n", "36 0.045676 15.366028 34.633972 \n", "37 0.049947 14.136648 35.863352 \n", "38 0.054219 13.091062 36.908938 \n", "39 0.058490 12.201794 37.798206 \n", "40 0.064897 11.067313 38.932687 \n", "41 0.071305 10.187242 39.812758 \n", "42 0.080916 9.163174 40.836826 \n", "43 0.090526 8.483581 41.516419 \n", "44 0.104943 7.807093 42.192907 \n", "45 0.126567 7.304364 42.695636 \n", "46 0.159004 7.121008 42.878992 \n", "47 0.207658 7.158215 42.841785 \n", "48 0.280641 7.118985 42.881015 \n", "49 0.390114 7.210452 42.789548 last reaction step" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history()" ] }, { "cell_type": "code", "execution_count": 8, "id": "4fa4035f-00eb-4cc7-a0ff-835bcc8baf52", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "From time 0 to 0.001, in 1 step of 0.001\n", "From time 0.001 to 0.0065, in 11 steps of 0.0005\n", "From time 0.0065 to 0.0095, in 4 steps of 0.00075\n", "From time 0.0095 to 0.01625, in 6 steps of 0.00113\n", "From time 0.01625 to 0.01794, in 1 step of 0.00169\n", "From time 0.01794 to 0.01878, in 1 step of 0.000844\n", "From time 0.01878 to 0.02005, in 1 step of 0.00127\n", "From time 0.02005 to 0.03144, in 6 steps of 0.0019\n", "From time 0.03144 to 0.04568, in 5 steps of 0.00285\n", "From time 0.04568 to 0.05849, in 3 steps of 0.00427\n", "From time 0.05849 to 0.0713, in 2 steps of 0.00641\n", "From time 0.0713 to 0.09053, in 2 steps of 0.00961\n", "From time 0.09053 to 0.1049, in 1 step of 0.0144\n", "From time 0.1049 to 0.1266, in 1 step of 0.0216\n", "From time 0.1266 to 0.159, in 1 step of 0.0324\n", "From time 0.159 to 0.2077, in 1 step of 0.0487\n", "From time 0.2077 to 0.2806, in 1 step of 0.073\n", "From time 0.2806 to 0.3901, in 1 step of 0.109\n", "(49 steps total)\n" ] } ], "source": [ "dynamics.explain_time_advance()" ] }, { "cell_type": "code", "execution_count": 9, "id": "09c03e23-0dd8-4ba0-a5b7-119f5662f23b", "metadata": {}, "outputs": [ { "data": { "text/html": [ " \n", " " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=A
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"white", "zerolinewidth": 2 } } }, "title": { "text": "Single reaction A <-> B (no downregulation) (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ -0.0001632277261263157, 0.39027749316802085 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -2.7777777777777777, 52.77777777777778 ], "title": { "text": "concentration" }, "type": "linear" } } }, "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_history(colors=[\"blue\", \"green\"], title=\"Single reaction A <-> B (no downregulation)\",\n", " show_intervals=True)" ] }, { "cell_type": "markdown", "id": "ce63f6dc-f9fc-4875-82aa-bbd05488ecb5", "metadata": {}, "source": [ "#### Notice the intersection at the exact midpoint of the 2 initial concentrations (50 and 0):" ] }, { "cell_type": "code", "execution_count": 10, "id": "477e29f3-17ee-4037-920a-b3e33920f04a", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Min abs distance found at data row: 27\n" ] }, { "data": { "text/plain": [ "(0.02453617850732098, 25.000000000000007)" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.curve_intersection('A', 'B', t_start=0, t_end=0.1)" ] }, { "cell_type": "code", "execution_count": 11, "id": "58b4b5e5-ebd0-4bb6-8059-6a460d555106", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: A <-> B\n", "Final concentrations: [A] = 7.21 ; [B] = 42.79\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 5.93438\n", " Formula used: [B] / [A]\n", "2. Ratio of forward/reverse reaction rates: 6.0\n", "Discrepancy between the two values: 1.094 %\n", "Reaction IS in equilibrium (within 2% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that all the reactions have reached equilibrium\n", "dynamics.is_in_equilibrium(tolerance=2)" ] }, { "cell_type": "code", "execution_count": null, "id": "00363317-fe95-4d18-acab-5e6116e01a17", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "3f67c102-0d90-4624-98f3-d6f50719d8c1", "metadata": {}, "source": [ "# Scenario 2: \n", "### downregulated by shunt: \n", "### kinetically fast, \n", "### but with thermodynamical dis-advantage (i.e. energetically un-favored)" ] }, { "cell_type": "code", "execution_count": 12, "id": "589fe009-4bf5-454e-ac37-9abd6ba7ffeb", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 2 (at temp. 25 C)\n", "0: A <-> B (kF = 30 / kR = 5 / delta_G = -4,441.7 / K = 6) | 1st order in all reactants & products\n", "1: A <-> S (kF = 150 / kR = 100 / delta_G = -1,005.1 / K = 1.5) | 1st order in all reactants & products\n", "Set of chemicals involved in the above reactions: {'B', 'S', 'A'}\n" ] } ], "source": [ "# Register the new chemical (\"S\")\n", "chem_data.add_chemical(\"S\")\n", "\n", "# Add the reaction A <-> S (fast shunt, poor thermodynical energetic advantage)\n", "chem_data.add_reaction(reactants=[\"A\"], products=[\"S\"],\n", " forward_rate=150., reverse_rate=100.) \n", "\n", "chem_data.describe_reactions()" ] }, { "cell_type": "code", "execution_count": 13, "id": "cb582868-431c-4022-aa0e-a2f554f80d6c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[GRAPHIC ELEMENT SENT TO LOG FILE `down_regulate_1.log.htm`]\n" ] } ], "source": [ "# Send a plot of the network of reactions to the HTML log file\n", "chem_data.plot_reaction_network(\"vue_cytoscape_2\")" ] }, { "cell_type": "markdown", "id": "b0345d36-5702-4b40-9221-a765dfcb0bac", "metadata": {}, "source": [ "### Set the initial concentrations of all the chemicals, in their index order" ] }, { "cell_type": "code", "execution_count": 14, "id": "ae304704-c8d9-4cef-9e0b-2587bb3909ef", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "3 species:\n", " Species 0 (A). Conc: 50.0\n", " Species 1 (B). Conc: 0.0\n", " Species 2 (S). Conc: 0.0\n", "Set of chemicals involved in reactions: {'B', 'S', 'A'}\n" ] } ], "source": [ "dynamics = ReactionDynamics(chem_data=chem_data) # Notice we're over-writing the earlier \"dynamics\" object\n", "dynamics.set_conc([50., 0, 0.], snapshot=True)\n", "dynamics.describe_state()" ] }, { "cell_type": "markdown", "id": "fc516ca2-e62d-4784-b826-5372ff7f4c75", "metadata": { "tags": [] }, "source": [ "### Run the reaction" ] }, { "cell_type": "code", "execution_count": 15, "id": "2502cd11-0df9-4303-8895-98401a1df7b8", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* INFO: the tentative time step (0.001) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 0.0005) [Step started at t=0, and will rewind there]\n", "* INFO: the tentative time step (0.0005) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 0.00025) [Step started at t=0, and will rewind there]\n", "69 total step(s) taken\n" ] } ], "source": [ "dynamics.set_diagnostics() # To save diagnostic information about the call to single_compartment_react()\n", "\n", "# All of these settings are currently close to the default values... but subject to change; set for repeatability\n", "dynamics.set_thresholds(norm=\"norm_A\", low=0.5, high=1.0, abort=1.44)\n", "dynamics.set_thresholds(norm=\"norm_B\", low=0.05, high=0.5, abort=1.5)\n", "dynamics.set_step_factors(upshift=1.4, downshift=0.5, abort=0.5)\n", "dynamics.set_error_step_factor(0.333)\n", "\n", "# The changes of concentrations vary very rapidly early on; automated variable timesteps will take care of that\n", "dynamics.single_compartment_react(initial_step=0.001, reaction_duration=0.3,\n", " snapshots={\"initial_caption\": \"1st reaction step\",\n", " \"final_caption\": \"last reaction step\"},\n", " variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "code", "execution_count": 16, "id": "a41e5009-e2b3-4bea-9892-7b9bd8295a07", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=A
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{ "text": "concentration" }, "type": "linear" } } }, "image/png": 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91PIkPnLMGLkX0LMSpqc+Iyth0eapRESYsn8icJlYmZj2yF3VPmdqc1LkFsZY1/Roc1U8W0SuSlq1Ehat7fG+Vz5QiCfy9dyval0JU2uf2vUiXj+Uc5/yhdxmnH9q9xHyPbMcVfueKWOld3SmnAiL5mSoBC4ML7YI9enZJaqzfaTBzbigqF18IicPrTd50dLpGdSxTnat7Yg2+UWKsFgCS947XJDXVLKHWoShyLbq2W+r56QR42Jw/x61zs94219E4lj9E7/LT4S1biuLJvISXRkzS9BpEWGiD7Hem6J17OgRYWacF7HsLdu5TUHzuKtDVoox5RPERELUC1/H009rVR1UR9lmPQ8PYjGLJsK02l/0Vc2/ycjNmpabWbX2ahUy8rmu5QGW3JZoZWsRYUtXrodYEWyUm1Pdtci5SCvnWHNYtBs9ue03jB2JwjkfavKhSVSERVtx0Hru6+mn1uug1rpj3fhpuc7EengQ2S8956+Re4HIew099cW6T9FzTyTmrz49u+KRZ16V0EZebxIRYfJ1Z8uPu6SyO7VvFfM9h1ofWMlzRLSX18diozZGEhVhWsddtLGr5i8fOZ7iLWLEu1eIxSxyntR6vVDrj5b5VOv9pJ57VOU9pHi/bFHxiWrBn3IiTNmZyG1OypvhyP3hyuhB0VbTIk8ypeLXslwp8kdulVQ7ceUb5cgbdtEuOdKUmoH1+jTFmnjlCUjc9MdqRzRFf8Odj9TZRqfGNfKCGm0iU2ur/F0822k9adQuzlovLPEu1vFEmtanMrJdtG65lcuV+2H1y5pjjZvIPuoZO7GedCovZomeF1rsnehFS+agZ9VeyU7Ol4j4UgoA8QqNyP38esdLrLkkmgjTan+1stXOp3jnYOT4U5s/op1fam2Q64tcodbbDrW+KLfTKOffyLGnNhYj69fKOdqNjvwASc3nQ9nOaGNIeYOl95qpxkbrfK68F4j0y1TjFq2fyboexzrnRNvEIYKW6Om/nDZyS7GoSxnVWMv5G82OylV9rfXFmmej3ROp3TvJK8hqPvKyPY34hMlzhdwf8bcySEfkXBJtjot2XdfLWzlfm70SpnXcReuLmr0iz69Y9tY6ZtTOWbWHolqvF2r90TKfGjn/4t2jym2R5xrltT0lRVjkDYYSttqWLrX9o2orFsoLiChTlCW/s0C5eqN8Sq2sW82XJNZTSiFkYrVdrT3yUqaWKHDxRJioW76Ax2pHZBoxgAb1O0t6YXHkxKXGRsk6sk9mvydMLfKW2osblcEJ4t3sall9lW/u9GyXijbpOeF7tXEht0uPz5TWsaNVhIk2JHJeaBFGWs4bJ9hIaxui2TLeuFeWH+siG+sGRav91dqotqVTvvGS5+dYN06yHUX0ruWrv6nuTrTxq7WtspiR3w+pZRtx5DVItEFsR5Ff+i62pcjlqt2EKf0X1eoz2nZRp+C8fec+RPNhiSZSop2Lsa6Z0YJ6REbjjeyPfA1R4yi/WzDymqgcK/H6qeU6mMi8ozyXItslflOOST03gWo2kOvS8uBYTqunb5Fp1eoT30XaKt57wiK5RJ6navYU9ShXpfWIeiW7eO//0vvgJd7DvmhsrFgJk+0Tb9xFu56o2VttDo3WJ61jVK19Iq/adUrr9UKtT/J8Jv8WOZ/qPf+06gvldUN5T5zSIkzrTYjZ6dLtJs1sPiyPBEgg/QjovRFJPwLsUSoT0Luakcp9NaPtattlzSjXSWVomdPiCapo/dFStpNY2N0Ws3ag2N0PvfVThOklFiMSjIGimIUESIAEUoaAHr+IlOkUG5p2BJRb++XORW6NT7tOJ9AhcV6L3S3yiqwoSmsgkQSqtTWrVnGViDjgfKndxIlw1l6L81JShBmwCVfCDEBjFhIggZQnIG+9UPPHTfnOsQNpQ0Btu5KebdRpA0JjRyK3aIlserYra6zGUcm0rFTJXIxGu+V8qd3kFGHaWTElCZAACZAACZAACZAACZAACZCAQQJcCTMIjtlIgARIgARIgARIgARIgARIwAgBijAj1JiHBEiABEiABEiABEiABEiABAwSoAgzCI7ZSIAESIAESIAESIAESIAESMAIAYowI9SYhwRIgARIgARIgARIgARIgAQMEqAIMwiO2UiABEiABEiABEiABEiABEjACAGKMCPUmIcESIAESIAESIAESIAESIAEDBKgCDMIjtlIgARIgARIgARIgARIgARIwAgBijAj1JiHBEiABEiABEiABEiABEiABAwSoAgzCI7ZSIAESIAESIAESIAESIAESMAIAYowI9SYhwRIgARIgARIgARIgARIgAQMEqAIMwiO2UiABEiABEiABEiABEiABEjACAGKMCPUmIcESIAESIAESIAESIAESIAEDBKgCDMIjtlIgARIgARIgARIgARIgARIwAgBijAj1JiHBEiABEiABEiABEiABEiABAwSoAgzCI7ZSIAESIAESIAESIAESIAESMAIAYowI9SYhwRIgARIgARIgARIgARIgAQMEqAIMwiO2UiABEiABEiABEiABEiABEjACAGKMCPUmIcESIAESIAESIAESIAESIAEDBKgCDMIjtlIgARIgARIgARIgARIgARIwAgBijAj1JiHBEiABEiABEiABEiABEiABAwSoAgzCI7ZSIAESIAESIAESIAESIAESMAIAYowI9SYhwRIgARIgARIgARIgARIgAQMEqAIMwiO2UiABEiABEiABEiABEiABEjACAGKMCPUmIcESIAESIAESIAESIAESIAEDBKgCDMIjtlIgARIgARIgARIgARIgARIwAgBijAj1JiHBEiABEiABEiABEiABEiABAwSoAgzCI7ZSIAESIAESIAESIAESIAESMAIAYowI9SYhwRIgARIgARIgARIgARIgAQMEqAIMwiO2UiABEiABEiABEiABEiABEjACAGKMCPUmIcESIAESIAESIAESIAESIAEDBKgCDMIjtlIgARIgARIgARIgARIgARIwAgBijAj1JiHBEiABEiABEiABEiABEiABAwSoAgzCI7ZSIAESIAESIAESIAESIAESMAIAYowI9SYhwRIgARIgARIgARIgARIgAQMEqAIMwiO2UiABEiABEiABEiABEiABEjACAGKMCPUmIcESIAESIAESIAESIAESIAEDBKgCDMIjtlIgARIgARIgARIgARIgARIwAgBijAj1JiHBEiABEiABEiABEiABEiABAwSoAgzCI7ZSIAESIAESIAESIAESIAESMAIAYowI9SYhwRIgARIgARIgARIgARIgAQMEqAIMwiO2UiABEiABEiABEiABEiABEjACAGKMCPUmIcESIAESIAESIAESIAESIAEDBKgCDMIjtlIgARIgARIgARIgARIgARIwAgBijAj1JiHBEiABEiABEiABEiABEiABAwSoAgzCI7ZSIAESIAESIAESIAESIAESMAIAYowI9SYhwRIgARIgARIgARIgARIgAQMEqAIMwhOma24JIjik+UmlMQi7CLg87jQMNuPn4vK7GoC6zWJQL0MD/w+D44eD5hUIouxi0BufR+CFSGcKA3a1QTWaxKBprkZOHaiHIFgpUklshi7CLRonIV9h0sQsqsBrNcUAh63C+K83H+kFAVNskwpk4XoI0ARpo+XamohwIQQ45G6BCjCUtd2kS2nCEsfW1KEpY8tKcLSx5YUYelhS4ow++1IEWaCDSjCTIBocxEUYTYbwMTqKcJMhGlzURRhNhvAxOopwkyEaXNRFGE2G8Ck6inCTAKZQDEUYQnAE1kfeughuN0eVFZWKEpyAQjB6/UhFApJv9XPzoHX40WgPICcBrnw+fxwu93Ia9ESa1ctR98BQ3G8uAjbtm5Bz179sXfPTulzyaL5GD1mAmY+/xQm33oPZs+ajktGj5PKeOu1l3DBqNFo2KgJ5r45E0OGjUSTZnl47+1X0f+8YcjLL8C8ua+jT//ByC9oJbXvixVL4fP7pbLFsWP7VmzcsA4jL71a+jsQKMMbhc9h4i13VPdHWbYS1+uF03D5NeORnZ1Ti2Lh9Kdw3aTbpHrko6KioroPysQlJ0/gndmFGD/59qiWeHfOLAwceiGaNc9XTfPl6s+kbRG9+g5U/f3ggX1Y9skCXPmLiVHrUIqwlcsXo352A3Tv2VvT6FDrb7SMwr5bt2zEiItHayo7MlGwvByvzHgWk6bcZSi/yKQcH4YLiZLxhWcfxc2/vt/sYnFg/16sWLoIV4yZELdsvSJsw/q1KD52FOcOGh63bL0JFi+ch7btTkeHTl30ZjUl/fv/no2z+w5AQcs2ppSntxDlfKU3r0ifbBGmZ5wZ6Y8VefTOV1a0QUuZZoswM+ZCLe0+VdNE3isoOVCEpceokEXYX//yZzz44IPp0akU6wVFWIIGowijCKMIqzmJKMJqTygUYTUPjYxMtRRh8alRhBl/IBWf7qmbgiIs/W1PEWa/jSnCErQBRRhFGEUYRVi0aYQijCIswUtM3OwUYRRhcQeJgQQUYQagpVgWijD7DUYRZoIN6BNmAkSbi6BPmM0GMLF6vdsRTayaRZlMINkrYSY3n8UpCJi9HZFw7SPA7Yj2sTezZvqEmUnTWFkUYca41cpFEWYCRJuLoAiz2QAmVk8RZiJMm4uiCLPZACZWTxFmIkybi6IIs9kAJlVvhwj7Yt1mPD59DqY9chca5daOJ2BSt5JSTElpAA8+NgP9e3XFVaMGG66TIswwupqMFGEmQLS5CIowmw1gYvUUYSbCtLkoijCbDWBi9RRhJsK0uSiKMJsNYFL1VogwWZy8//HKWq38y/2TJbFipwgTdU99+AVMf/QedGhbkBBFirCE8JmXWfiEAR4AjI4oU2V0xOjji9ERjZ17eqLW6RVhjI5ozCZacjE6ohZKiaWhTxh9whIbQeq56RNmBVVnlWm2T9jWn/Zgyv2PY9Swfrh7ytjqzh4pKsbUv72A+24bh8NHjnElTDEMuBKW4DkhRFgo5IHLRRFGEVYTkj/asKIIM3bCUYQZ48YQ9fq46Rln+kq2LjVFGEWYFaOLIswKqs4q00wRJq8M5TdvXEuARfZYXgm7Z8pYaVVq7/5DUpLCpx5An56dawm3Wx94Et9s+lH67pLh/fHQfZORlemHEHXit0m/GImX3/ywOo1Ybetx5umSEFQrV20VThaOcvruXdpLWyXFoaxf/H3jtaOq+8aVMIeMZYowRkdkdMSak5Eh6mtPTIyOyOiIVl+qKMIowqwYYxRhVlB1VplmijBZzDw89eZaYkpNhN1w5yO1RNXc+UsxZ96Saj8xWWQJoSYLsyemz8G+A4clIVZaViYJJHHIvmVCYIlyZREl/M0iRVfk32ptXrBkNU4/rRUaN8zBy7M/wK0TR9cSfmMvGyptq6QIc8hYdrmAM7uFsHBJqUNaxGYYIUCfMCPUnJlH73ZEZ/aCrRIE6BOWPuOAPmHpY0v6hKWHLc30CdPqbxVtNeoPD7+A/516s+SrJUTZ9p37aq2oCcEkpxECSYgwpUhTE26R30XWLYSdOJRbJ2NZVtkuijCHnANChDVpCny9ucQhLWIzjBCgCDNCzZl5KMKcaRcjraIIM0LNmXkowpxpFyOtoggzQs15eZwqwoQ4eumN+XWAtchrIgXVMEOEZWZkSNENx1w2NOrKXeRWRdEgeVuk+DejIzpgTAsRJo7dBynCHGAOw02gCDOMznEZKcIcZxLDDaIIM4zOcRkpwhxnEsMNoggzjM5RGc0UYXq2I0aGqFeucomVsHgrVFpWvQToWCth8USYWPX606Mzavmqie9Wrt0obYmkCHPIUBY+YRUVHng8DMwhm4TREaMPTgbmMHbi6gmYoFeEMTqiMZtoycXoiFooJZaGPmH0CUtsBKnnpk+YFVSdVaaZPmHxAnPIvlZq0REjRZhS7IhAHJGHGSJM+IzFEnvit3at82u9A4wizFnjV2oNRRgDczAwR82JycActScpBuZgYA6rL1sUYRQCY6iOAAAgAElEQVRhVowxijArqDqrTDNFmOhZtBD1QtDMX7xK2kqoRYSplSNE3rSZ72LSuIsliGb4hMnBPJSRGWWx+N6Hy6sDgQghKLfpnG4duRLmpGFMEUYRRhFGERZtTqIIowiz+npFEUYRZsUYowizgqqzyjRbhIneqb2sOVbEQlm8KQNziO/k1S45RL34Tg4Rb9ZKmChTFmKyZeS2ytsV5ZdOC1+ws7p2wNcbt1KEOWkY/+pXwPTpwGNPBvDLCcotiU5qJdsSjwB9wuIRSp3f9W5HTJ2enXotpU9Y+ticPmHpY0v6hKWHLc30CUsPIsnvBV/WnCDz//kfsSURuH9qOe64J5hgacxuFwGKMLvIm18vRZj5TO0qkSLMLvLm10sRZj5Tu0qkCLOLvLn1UoSZy9NIaRRhRqgp8ohVMLEadsONQfzv/5UnWBqz20WAIswu8ubXSxFmPlO7SqQIs4u8+fVShJnP1K4SKcLsIm9uvRRh5vI0UhpFmBFqijz0CaNPGH3Cak4IBuaoPaHQJ4w+YQleYuJmp08YfcLiDhIDCegTZgBaimWxwicsxRDY3lyKsARNQBFGEUYRRhEWbRqhCKMIS/ASEzc7RRhFWNxBYiABRZgBaCmWhSLMfoNRhCVoA4owijCKMIowijB1AnxPWIIXGA3ZKcIowjQME91JKMJ0I0u5DBRh9puMIixBG5SXA34/4PUBP+0tSbA0ZreLAH3C7CJvfr30CTOfqV0l0ifMLvLm10ufMPOZ2lUifcLsIm9uvfQJM5enkdIowoxQi8jTuDFw5AiweVsJcnJMKJBFJJ0ARVjSkVtWIUWYZWiTXjBFWNKRW1YhRZhlaJNeMEVY0pFbUiFFmCVYdRVKEaYLl3riLl1D2LzJhWUrS9H+9JAJJbKIZBOgCEs2cevqowizjm2yS6YISzZx6+qjCLOObbJLpghLNnFr6qMIs4arnlIpwvTQUkkrfMJCIQ9cLuWLml0AQvB6fQiFQqisrED97Bx4PV4EygPIaZALn88Pt9uNvBYtsXbVcvQdMBTHi4uwbesW9OzVH3v37JQ+lyyaj9FjJmDm809h8q33QOlj8dZrL+GCUaPRsFETzH1zJoYMG4kmzfLw3tuvov95w5CXX4B5c19Hn/6DkV/QSmp95D7vHdu3YuOGdRh56dXS74FAGd4ofA4Tb7mjurfKspUIXi+chsuvoU8YfcJqRgWjI9aeJBiYg4E5ErzExM1OnzD6hMUdJAYS0CfMALQUy0KfMPsNRhGWoA0owijCKMIowqJNIxRhFGEJXmLiZqcIowiLO0gMJKAIMwAtxbKcSiLsSFExbn3gSbQpaI6H7puMrEy/I6xFEZagGYQIAzwAuBImo1QTJRUVFdWreUrkJSdP4J3ZhRg/+faolnh3ziwMHHohmjXPV03z5erPIDaB9uo7UPX3gwf2YdknC3DlLyZGrUO5HVHvTQ1FGEUYRZg6AUZHTPACoyG73vlKQ5GWJDF7O2KwvByvzHgWk6ZQhFlhMIowK6g6q8xTSYR9sW4z3pq3BMeOn8R9t41Dh7YFjjAGRZgJZvjfv1Xgj3/w4Nd3BDH1T+UmlMgikk2APmHJJm5dffQJs45tskumT1iyiVtXn9kizLqWsuR4BOgTFo9Qavx+KvmEPTF9Dgb1OwvLVn2Ndq3zcdWowY4wEkWYCWZ4cUYFbr7Rg7HXVuDJZwImlMgikk2AIizZxK2rjyLMOrbJLpkiLNnErauPIsw6tskumSIs2cStqc8KEXb8OLBmjTXtjVVqdjbQu7d6CrEV8eGnX8PU316HH7btllbEnLIlkSLMhLEy7/0gLr/Ui/OHV+LVN8tMKJFFJJsARViyiVtXH0WYdWyTXTJFWLKJW1cfRZh1bJNdMkVYsolbU58VImz9eqBnT2vaG6vUHj2AdevUU4itiGIF7O4pYyH7ht0zZSz69Oyc/IZG1EgRlqAJhE+Yy+VBKESfMBklfcKiDyoR/XLrlo0YcfFoQyPPDD8IZfRMQ42IkYnREWvDYWAOBuYw+xyLLI8+YfQJs2KM0SfMCqrOKtMKn7CtW4Gbbkp+Pzt0AF58sW69JaUBPPjYDIy5bGi16BJbE8UhRJndB0VYghYQIszt9khh6GsOhqi/btJt8Plros8wMEd4dFCEGTvhDuzfixVLF+GKMRPiFqB3JWzD+rUoPnYU5w4aHrdsvQkowijC9I4ZvekpwijC9I4ZLekpwrRQSu00VogwpxHZ+tMeTLn/cezdf6hW07p3aY9pj9yFRrk5tjaZIixB/BRhDFHP6Ig1JxFXwmpPKBRhFGEJXmLiZqcIowiLO0gMJKAIMwAtxbKcCiJs7vylWLl2Yy0fMLXVMbtMRxFmAvnik+Xo3MmLPbtd+OrbEjTPM6FQFpFUAvQJSypuSyvTuxJmaWNYeEIE6BOWED5HZaZPmKPMkVBj6BOWED7HZLbCJ8wxnQMgi63+vbrWiYYoxNn2nfts35JIEaYYMbLBxFfKyCnCWH96dIaU8pLh/etEVREibMggD7760o0Fi0vR7Szx1ioeqUSAIiyVrBW7rRRh6WNLirD0sSVFWPrYkiIsPWyZ7iIsFaxEEVZlJVmAvf/xylpCS0RVeXz6nOq9o2oOfUKEXXO1Gws/9OCV2WUYNqIyFWzPNioIUISlz3CgCEsfW1KEpY8tKcLSx5YUYelhS4ow++1IEVZlAyGuxAvcxKHcPyp/L7/YLVKU0SeMPmH0CauZyOgTVntSp08YfcKsvszTJ4w+YVaMMfqEWUHVWWWeCj5hziJetzUUYQCUq1tKJz6BS4S2VO4nFZFW/vDwC/jfqTejQ9sC6BJhXi8CgQByGuTC5/PD7XYjv6Al1qxcjn4Dh+J4cRG2/bAFPXv3x97dO3F2n/74ZOF8XPmLCXj5uadw0+334PXC6bjsqnFSGW+++hIuHDUajRo3wTtvzMSQESPRtFke3p3zKs4dNAx5LQrwn7dfR58Bg9GioJVk/dWfL5WiFp7du7/0947tW/Ht1+tw8eVXS38HAmV4bcZzmPSrO6pHi7Js5RB6bcY0XDFmPLJzakeXmfHcU5gwuW50RLkPyjJKTp7AW68X4vqbbo96rsx9cxYGDb0QzfLCIjnyWLvqM4gNoL37DVT9/ecD+7B08QJcPW5i1Dp8bhca1PfjUHEZPl+2GNnZDXDW2VHe/FerFBdmPPckJky+vVY0yGgVbfvhO3y/ZZNkNyOHCFE/88VncOOtdxvJLuV5d84rVeOjpeEyomWc/vT/Ycpvf2d6uQf27cFnSz/GlWPjR0fM8rvh93pQdLJcUzu+WbcGxceKMGCw/uiIIg5qrGPRh/9Bu/YdcXqnLpraYnai/8x9A737DkRBqzZmF62pvNcKn8PlV10rzVdGjpwsL8orQigNKKPPGilJWx4xzpYv/RhXaRhn2kq0PlV4vsrBWWf3sb6yBGpolOPH8ZPlkj3NOMRcWPjiM7gpgbnQjHakaxmrPv8Ufn9G9b2Csp/NG2biwNHSpHTdnNGSlKamXCUeF9C4QQb++pc/48EHH0y59qdDg095ERbpnKcmwpTvF1ATYR6PByIEu3y4XC6EQiH4fD7pU/yWk9MAPp8XZWVlaNiwEfz+sAhr3bo1Pv10CYYPH4GioiJs3rwJAweeh59++kn6/M9/3sXkyTfh0UcfwdSpf8Czzz6N8eOvR8OGDfHcc//CNdeMRdOmTfHii8/j0ksvR35+PgoLZ2DEiAvRqlUrzJpViKFDh6FNm/BN2CefLJbqFmWL44cfvseaNWswbty10t+ifU8//RTuu6/mRlpZtnLQi3Q33DAZDRo0qHUuiLbeeefdUj3yIRjIfVAmPnHiBJ5//jncddc9Uc+nGTNexMiRo1BQUKCaZunST6XvBw8eovr73r17MX/+f3HjjTdHP2ddgNsFVFYCH320UOpTv35hoRr7COHRR/8Pd955V63+Rssj7Lthw7e45ppr4hWs+nt5eTmeeOJx/O53DxjKLzIVFr6MESMukMaH2cdf//oX/PGPfzK7WOzevRsLFy7ApEmT45Ytzj+4gFCltsv36tWrcfToEVx44UVxy45MEK+Gd/89Fx07nYEzzzxTd9lmZHj1lVcwaPAgtG3bzozidJfxz2efwXXjJ0jzlZHD7XYhWBGSzs1kHHt278YCjeMsGe3RUoeYr3Ib5KJvv35aktuWRjx1F6ekuCaacYi58MknHsf9CcyFZrQjXcsQ9woZ/gwMGFj34abH7UZlZaX08NPqI0mnvtXdcGb5Lpc0t/75zxRhdhnolBdhYhXspTfm1+EvAnA88JvxeOSZV2OuhImMwifsrXdCuPF6Py69ogLTXwrYZU/Wa5AAfcIMgnNgNvqEOdAoBptEnzCD4ByYjT5hDjSKwSbRJ8wgOIdlo0+Y/QaxVYQdKSrGrQ88iW82/ViHhF0vUot8p0A8nzBZhH26vBKXXZSBfudWYu68MvstyxboIkARpguXoxNThDnaPLoaRxGmC5ejE1OEOdo8uhpHEaYLl2MTU4TZbxpbRZhapEG7kUSKMK3RETdtqUC/szNxWvsQlq9Ozl5pu1mlU/0UYeljTYqw9LElRVj62JIiLH1sSRGWHrakCLPfjraJMLEKNvVvL+C+28ZJAS6ccqi9XTvWe8J0BebweBEorx2YI69FS6xdtRx9B1QF5ti6BT179cfePTulzyWL5mP0mAmY+fxTmHzrPZg9qyba2FuvvYQLRo1Gw0ZNMPfNmRgybCSaNMvDe2+/iv7nDUNefgHmzX0dffoPRn5VYI7IiEciMMfGDesw8tKawBxvFD6HibfUBOZQlq200+uF03D5NYyOyOiINaOC0RFrz2SMjsjoiFZf2xgdkdERrRhjjI5oBVVnlcnoiPbbgyIsQRtQhFGEUYRRhEWbRijCKMISvMTEzU4RRhEWd5AYSEARZgBaimWhCLPfYLaJMNH1SH8r+3HobwFFGEUYRRhFGEWYOgHlyr3+2RVI9nbEA/v3YsXSRbhiTPxXIRjpjxV5KMIowqwYVxRhVlB1VpmngghTiz1hV8wJNevbKsJEuPfX5i7CfbeOQ1ZmTThzZw3T+K0R0RGLS4IYd7Ufyz714KVZAYwclZz32sRvHVNoIUCfMC2UUiMNfcJSw05aWplsEaalTUxjjAB9woxxc2Iu+oQ50Sr623Qq+ITJIuyeKWPRp2dnCZKT4lHYJsJiRUYUkJykVOMNbVmE3flrP96a7cHfnwrg2vEUYfG4Oel3ijAnWSOxtlCEJcbPSbkpwpxkjcTaQhGWGD8n5aYIc5I1jLflVBVharEfjFNMLKdtIiyxZjsrtyzC/v6IF0/+3Ye77i3HvQ8EndVItiYmAYqw9BkgFGHpY0uKsPSxJUVY+tiSIiw9bGmFCDseOI41e9YkHVC2Pxu9C3rXqTfaSli71vm4atTgpLczskKKsARNQJ8w+oTRJ6zmJGJ0xNoTCgNzMDBHgpeYuNnpE0afsLiDxEAC+oQZgJZiWazwCVu/fz16Ptcz6SR65PXAul+tiyrCIt9H/Jf7J1OECVriPVw33PlILXCFTz1QvXcz6ZbUWaGaCAuFXHC5QvB6fQiFQqisrED97Bx4GaJeCrOvPEpOnsA7swsxfvLtUcm/O2cWBg69EM2a56um+XL1ZwgB6NV3oOrvBw/sw7JPFuDKX0yMWodyJUzvTQ1FGEVYtIFFEUYRpvOSoju53vlKdwUmZTB7JSxYXo5XZjyLSVMowkwyUa1iKMKsoOqsMq0QYVuPbMVN/7kp6R3t0KgDXrz8xagiTOkTprY6lvQGV1Vo60pY5IuQRZtEsI4p9z+O2yZe4QiVGs8wFGFcCaMIowijCFMnwOiI8a4gif9OEUYRlvgoqlsCRZgVVJ1VphUizFk9BKIJLqdEZ7dNhJWUBvDgYzMw5rKhdVa9hDh7a94SPHTf5JSImij7hInBd/aZWTiwH1j1VSlatRbrMzxSgQB9wlLBStraSJ8wbZxSIRV9wlLBStraaPZKmLZamcoKAvQJs4Jq8su0wics+b2IXaOaCONKGMLqdOrfXsB9t41Dh7YFtSiK1bDH/jUbD//+ZjTKzXGaTeu0RynCrrkiAys+c+P1t8ow5PxKx7edDQwToAhLn5FAEZY+tqQISx9bUoSljy0pwqy3ZVlFKSpDlVX/hVAZqgj/W/wvVIlQ9W9VaaD8LoSKyopwmqr0clnV+VAJF0LIqe9BFvLQr104fHu6HdEisTvF7YkrYSaMOKUI+93dPrw6y4u/PFyOyTczQqIJeJNSBEVYUjAnpRKKsKRgTkolFGFJwZyUSijCkoI5aiUlwZMIVlYgWFmOYCiIisogyivLqz6DqAgFEawMIlhR87tIX33zrriZb5jtxaFjpagQwkDxveQDL4sDFbEgCYNaoiCcvo5YqKpXLr9GcNSUX7ucSsn3XilSwuVGb49UtkgT0Z5wnpqyqsWMUvRECB5lH+RyawmlWixq2iSElhOO+/r/Pzx60UNOaMop1wbbRJggLWL1z5m3BNMeuat6xYs+YVvQs1d/7N2zU/pcsmg+Ro+ZgJnPPyUFtVD6WLz12ku4YNRoNGzUBHPfnIkhw0aiSbM8vPf2q+h/3jDk5Rdg3tzX0af/YOQXtJIGd+Q+7x3bt2LjhnUYeenV0u+BQBneKHwOE2+5o/pkUJatPENeL5yGy6+hTxh9wmpGBaMj1r6GMDAHA3NYfVdBn7DEfMJOBk8gWBGUhIkkUIQQEf8WYkSIllD4uxrRUhEWLxGiRSlwwnnDwqZckVcWOOF6KsK/V1QJoVD4U3xfI47keipqiSO5/vKKcLtEe2vlqayA6FcixwiMQClKsRzLEymGeRMgkOHJhNvlrvpPBHxzw+PywC3+53JLf9f8Ln2r+M4Fj9sT/rsqvZxWzudxueH3enHBzhF48MEHE2gpsxolYKsIk0QBoyNi7arl6DtgKI4XF2HbVoqwyMHM6Ig1RMyICKYU6UYnjmj5KMIowpQEGJjD7DOsbnlOFWHFgWIEKssQCJZJn1lZIRwuPoETgRKUVwZQWhH+TawGBCoCCFSIf5dJn+Lv0mBJ1d/h3+Tf5TQVwSAG7u6HD/MWVQuQsICqEk9VgkoST1UCR4iW0ooS643iwBrEDb3X7ZVuzH0uHzxuL3weHzwur/S99J+r6ju3F92Od0XQHcRPDXZW3+i7qm7ms/w+lAdDNUIAVeJAEgauGmEQQyy43Z5qcVEtKJRiofp3WUTUTi/liRAXcjmSUKkSKNraU5M+nC8seKR/y3Uo21P1fY0ICvdZKXjkNkSWE/67hpGwi13HqRCYwy62Wuu1XYRpbahT00WLjgiE4PMxRL1st4qKiurVPKUtGaJe38imCJsQF5je7Ygb1q9F8bGjOHfQ8Lhl603AlTCuhOkdM3rTCxGWVT8bHbufiUAwIAmeUiFsqv4tCR1JDIV/KwuWokyIHoVAKgsGJDEkfpMEkZQuLJ6kzwiBJP6W6qgSTzW/hwVTSHppiLWHH37ci3vxN/zNUEUuuOD1+CThoRQh0ndCrAhBIn8KsVIlUrxu8bsH4U9ZvFT92xMWMpLAcSsETtX3Po+/pmxPVTpXVX1yHlG21Ca5fPn32uKppp6qttZqY7hdssAyAojREY1QS608FGH224sizAQbKH3CKiqA0wqyID637SmB329CBSzCcgL0CbMccdIq0CvCktYwVqSbQLr5hIktYifKT6CkPPx5UvEpfHZOlB+Xvjsp/h0oVklTUvN9MJy/OHBMN9dkZKjnrY8Mbwb8ngxkuDOQ5c+E1+WHECLi6X+Gxy/9Jv0u/u3OQIY3s+o7PzI9mfBL+eX04bTi73Ae8V+mtLIjiZYq8eSVRI0QSTVCRhJF0uqPB/V92cnoflrXwcAc6WHeUyE6otMtRRFmgoWUIkwUN3RAJr7f4sKHH5eiew/rnwia0IVTvgiKsPQZAhRh6WNLO0SYcKgPC6Tjkl+NLJYkcST9VyWWqoRSzd/y78o8J6vKEZ8nLFshElufJGEiRIskZsRnjcgJC5qw0BHCRogi8bcQMeH0VSLIV/W3oiw5nyhTSi+LoKoyZPEkRJEsmNRGIANzpM95SRGWHrakCLPfjkkXYXK4yEm/GImX3/wQ32z6UZVC9y7tawXssB9V9BZEirAbr/fjw/ke/HN6AKOvrnBy09m2KgIUYekzFCjC0seWRkWYiFBWVHYURWVHUFR6FEcDR1FUegRHS4+gKHAUR0uOSL8dLTsa/k6kk9IflVajrDoyPVmo56uH+v5sZHnrSasy0t/i01sf9Xzh/+pL/4nf6qOeP/x3+Pd6qFeVVvrOVx/Z/hzJWd/pB0WY0y2kvX0UYdpZOTklRZj91km6CJO7HOs9Yan0smY1nzCIty+ExAqYD15vSAqdWj87B16PF4HyAHIa5MLn88PtdiOvRUsG5phdiPGTb496NjAwRw0a+oTRJ0zPZeP9f8/G2X0HoKBlGz3ZTEubSGAOsSIF7wkcPHkEe4sOVouqsGgS4umwJKLkf8siSggqERTCyNEKrTASIzHbNxtZshCSxZK/HrK8VYKoSigJYVTfn6MQUlUiyS8Lq/BnuKz6EH5IZh9ODcwR2U+zRZgZc6HZtkin8ugTlk7WVO8LfcLst7EjRVgqvaw5lgirrPTB76cIE8OcgTnCJ7uIfrl1y0aMuHi0obPfjBsPRkesjZ6BOQwNRU2ZhAgbMuoSlGcEpRUpSTCVHa7+95HSw1UiSrEaJa1cHUFx2THD2/dEpLIcfwPkZjRCo8xGyM1oKP1b+sxsiEaZTdBQ+q7q+8yGaJjRCMGiANavWIErxsQX+5oAJCERRVhiIeqTYKKUrIIiLCXNpqvRFGG6cFmS2JEiTLw/bOXajXjovsnIynR2ZItYIqyiwoeMDIowirCac5cizNg8dmD/XqxYukjTzbHe7YgUYdptIlaYjpQexOGSQzhceqjq8yAOldR8d0T6Lfz3hNLxKEQhjuKo9kqqUopVIyGkGmY1RK6/tpBqWCWkZFEl/S6EVGYjNPQ3Qk5GA0OrTnrGme4OWZSBIowizIqhRRFmBVVnlUkRZr89ki7C5Jcx791/KGrvW+Q1wfRH70GHtgX2E9LQgkifsMOHgO5nZEmREUWERB7OJ0CfMOfbSGsL9YowreWmWzoRfvzgyZ9riSlJWJ08WPu7kkOSyDpSdhjlFQHdGLJ92cgVq1H+sEgS/27oD69INcxsLK1AiX8LISXElZTG3wgNMnLRKDsDwYoQTpQGddfLDM4iYPZ2RGf17tRqDX3C0sPep4pPmJruuPHaUbh7yljbDZl0ESb3OJZPmO1UdDYgUoSJ7Ge0y8Tx4y58sb4UBS0ZIVEn0qQnpwhLOnLLKjzVRdj2oq3YXbwLe47vwr4Te3DgxH4cFitVEStYRl5aKwJLNM5qgsaZTaTPJllN0SizKZrWa4ZGmY2rfmtanaZ5vfyE7Gw0MEdClTKzJQQowizBakuhFGG2YDe90lNBhMnBAO+ZMhZ9enaWGJaUBjBt5ruYNO5iNMrNMZ2rngJtE2F6Gun0tGoi7PKLM7D2CzfeeLsMg4dWOr0Lp3z7KMLSZwikswgTwkr8t7t4J/Yc3409x3Ziz4mqv4t34VDpQV2GbFYvD00yZdEU/hTCSnwKcSWLLfHZMqe1rrLNSEwRZgZFZ5RBEeYMO5jRCoowMyjaX8apIMJEoL/Hp89xbLR1irAEz4NoPmFACIFAODCHy8XoiAzMER5o9AkzdsLp8dXRK8Kc4hN2sORnSWDtkVaxdmLv8T3YdWwH9h7fjV3Hw59ajhbZLVGQ3Qots1uj2/7O8LbLQuO85rVWsBpnNpX8raw+EomOKNqWbBGmZ5xZzU5r+fQJo0+Y1rGiJx19wvTQSs20lviEHT8OrFmTfCDZ2UDv3nXqlbcijhrWzxHbDyMbaKsIi+UflirvCYsnwny+ENxuijCKMIqwRGZlPTfHThRhLdq3kQSVvIoVXskKr2rtKd4tfZZVlMZEJAJViFUqIbAKclqhILu1tDpVkFMjuvLqt4CIDCgfqRyiniJM2xlDEUYRpm2k6EtFEaaPVyqmtkSErV8P9OyZfBw9egDr1qnWq6Y1Cp96oHp7YvIbW1OjbSJM7Ml88LEZ6N+rK3qceTpem7sI9906ToqG+MT0ORjU7yxHAIpnnHgiTLwnzOOhCKMIowiLdy7F+t3JIkwEq9h9vGp7YPEu6d+SyCrehXb7W+Gb4NdYUxH/yaBYmZLEVf2wyGrVoE31vwuyW0orWz6PvmixFGH6Rp2ecaavZOtSU4RRhFkxuijCrKDqrDItEWFbtwI33ZT8jnboALz4oqZ6RQT2f818zxEBAG0TYcrAHILaY/+ajYd/f7PkJJdKL2sWbVfzCdvynQvnD8yUgnKI4Bw8nE2APmHOto+e1uldCYtVtnhhsAhuoVy12i1WtE7I2wZ3QWwjjHdkeDIhtgm2lFawwv+JVSxpJSs7LLjEi3951CaQ7O2I5G8dAfqEWcc22SXTJyzZxK2p71TwCVMjpxaswxrC8Ut1hAhr3DAHDz/9Gqb+9jpJhKXSy5qjibCKCqBNXpZkARGmXoSr5+FcAhRhzrWN3pbpEWElwZP44cgW7C5WbhXchX3CH0unH1ar7DaS0BLbA2VxVVAlsppmNdPbDaa3wSeM0K0jQBFmHdtkl0wRlmzi1tR3KogwsaizbNXXtfzBnBSswzYRptyOeNWowdIWxHat8yH+nUova44mwsT3A3pn4qftLiz8pBRndmeYemumEXNKpQgzh6MTSokUYUJofX/kO/xU9CO2F/2IH49+j5+ObpM+fy45ELfJInpg69x2yKuXL20JLGggVq9aolVOlejKbhW3DCYwRoArYca4OTEXRZgTrWKsTRRhxrg5LdepIMLkVa9vNv1Yjd9JMSdsE2GRg1EJKpVe1hzLJ5TYOwEAACAASURBVKyiwodQKASvtwLZOTnwerwIlAeQ0yAXPp8fbrcbeS1aYu2q5eg7YCiOFxdJ0fN69uqPvXt2Sp9LFs3H6DETMPP5pzD51nugjDb21msv4YJRo9GwURPMfXMmhgwbiSbN8vDe26+i/3nDkJdfgHlzX0ef/oORXxC+UYzc571j+1Zs3LAOIy+9Wvo9ECjDG4XPYeItd1SbSFm20m6vF07D5deMR3Z27fcsFE5/CtdNug0+xfIffcLC5Bgd0dhlKJ6vzsngCXx/+Dv8dOxH7Dm+HduKtuL7gz9oElqjMi9Bga8lTrYuD/thVW0VbJFdgNNyTzfW4KpcixfOQ9t2p6NDpy4JlWM0M33C9JGLN870lZac1PQJo0+YFSONPmFWUHVWmZb4hDmri45vjWNEmONJRWlgLBEWCvkQDIbg81GEUYRRhCVyjoub4+WfLkTH83tAvIxYiKxtR3/AtiNbpb9jrWh53T60adAO7XLbS6LqtIYdcFqj03Fabnu0ymmLTV+vQ/Gxozh30PBEmqialyJsOi4ZPU568GTkSPZKGEWYEStpy2P2SliwvByvzHgWk6ZQhGmzgL5UFGH6eKViaoow+61mmwhTBubo0LbAfhIGWxBLhLlcPgQC4ZWwnAZcCZNX85SoS06ewDuzCzF+8u1RLfDunFkYOPRCNGuer5rmy9WfQWz27NV3oOrvBw/sw7JPFuDKX0yMWodyO6LeJ8tqK3/RKuJKmLYTTQTC2PDzemw4uB4bDqzDgf170OvkOXgR6tGPZKF1Wm4HdGx8Os5odgaaZ7VF+9wOaJnTBh6XJ2rFTnlPmDYy+lJxJUwfL4owfbz0pKYI00PL/rQUYfbbwOoWUIRZTTh++RRh8RnFTaEWHVFk2rXThX5nZ0r5dx8siVsOE9hHgD5h9rAPIYQfj/6ADT+vq/pvvSS+DpceqtMgpdBql9sB7RudjnYNO9QRWnoCc9jTa9aqlUCyV8K0tovp9BMwW4TpbwFzmEWAPmFmkbS3nFPBJ8xewvFrt02Eiaal0vvAYqGMJsJEnp5dM/HzARcWLS1Fl64MzhF/SNqTgiLMeu7ifVrfHdkkiaxvDnwlfW48+A2EP1fkke3LRtemZ6Fb0x7oltdT+jyjcRcIIRbvoAiLRyh1fqcISx1bxWspRVg8QqnzO0VY6tgqVkspwuy3o60iTISiV76k2X4cxloQS4T9eoof/37Hg78+Uo5JNwWNVcBclhOgCDMX8Yny4/j24Nfh7YT710mf3x3ehGBleZ2KRPTBbs174MymPdC9eU90b9YTYqXLBZehRlGEGcLmyEwUYY40i6FGUYQZwubITBRhjjSL7kZRhOlGZnoG20SYWthIZe+cFEIyFvVYPmFebzgwRyhUgUAgB3l5jI4oIjwqD/qE6TunzXBGV0bP1Fe7eupDpQex4cB6fHtwPXyfBzEz91UpWIbYahh5iLDu3Zr1QLdmYbEl/p1fP75PqB5fHb0ijD5hZowC9TKU0VyN1JJsEaZnnBnpjxV59PqwWtEGLWWaLcLMmAu1tPtUTUOfsPS3PH3C7LexbSLM/q6b04J4IqyyMgQRGbC4uAHatPEwRD1FGLZu2YgRF482NADNuPFIRITtKt4h+W59cyC8uiW2FO47sae6L/+D8P9EIIz2DU+XRFb35mejW9Ow4MrNaGio33pujinCahAzMIe+4aZnnOkr2brUFGGMjmjF6KIIs4Kqs8qkCLPfHraJsFjREcXbrN+atwQP3TcZWZl++ynFaEE8ESbeExYMVqCoqAEKWooIbXxPGFfCnC/CKkOV+OHIFml1Kyy4ROCM9SgqO1rnbPC7M9C5SVdpdavTxrbodc1QdG3WHZmeLNPOXT03xxRhFGFGB56ecWa0DrPzUYRRhJk9pkR5FGFWUHVWmRRh9tvDkSJM+Io99q/ZePj3N6NRbu0XAduPrG4LYvmEidS33eLHe3M9ePixclw/iX5hTrThqewTFqgsw6aD30qC6+uqgBmbDm5AaUXdiJ45/hx0FcEyqvy3xOpWx0ad4XV7HWNWvSLMMQ1nQ+oQSPZ2RJrAOgJmb0e0rqUsOR4B+oTFI5Qav9MnzH47OVKEzZ2/FCvXbkyJlTBhwngibFahF1Pv9eHyKysw7YWA/VZnC+oQOFVEWFlFKdbtX4Ovf/5KWuH69uevsfnwt6ojQgTMEH5bZzbvgZ7Ne6FL027Sy46dflCEOd1C2ttHEaadldNTUoQ53ULa20cRpp2Vk1NShNlvnaSLMLHKNeX+x7F3f933AMk4WuQ1wfRH70GqvMQ5ngj7fosLQwdkolnzENZtLLXf6mzBKSPCDpb8jC/2fI6Vez7Dl/tX48t9q1Wt37pB21rRCc9sepamgBlOHEoUYU60irE2UYQZ4+bEXBRhTrSKsTZRhBnj5rRcFGH2WyTpIkzuciyfMPuxaG+BFp+wysqwT1gg4EXLlmVo2DgXPp8fbrcbeS1aYu2q5eg7YCiOFxdh29Yt6NmrP/bu2Sl9Llk0H6PHTMDM55+CiCyojDb21msv4YJRo9GwURPMfXMmhgwbiSbN8qAMvDBv7uvo038w8gtaSZ2K3Oe9Y/tWbNywDiMvvVr6PRAowxuFz2HiLXdUQ1CWrSTzeuE0XH7NeGRn194yWjj9KVw36Tb4/DX+fCI4idwHZRmMjqh9rImU8QJzbDq0Aav3fC79JwTXjuLttSro2OgMXHJiFH7OO4z2bTrjrOZnS6tdOf4G+hoSJfULzz6Km399vyllKQvR46ujV4QxOqLp5qoukNERrWMrl0yfMPqEWTHK6BNmBVVnlUmfMPvtYZsIs7/r5rRAqwgrLctB8TEfmjUrQ/N8ijCZPkWYvnGoFGHCZ+vLfV/gi70rJNG1dt8qFAeO1RFd/QrOw7mtBuG8VuejaVazWiJdX+3xU1OE1Wa0eOE8tG13Ojp06hIfngUpGB1RH1Q9Yl9fydalpgijCLNidFGEWUHVWWVShNlvD4qwBG2gVYQBOfj5Zx9yc8vQqg1FGEWY/hD14gXIy35ajJ8WbsK/m7yHb35eV2f0ntGkKwa2HIp+LQdIn40yG9dJk0iI+ninC0UYRZiSAFfC4p0xif9OEUYRlvgoqlsCRZgVVJ1VJkWY/fawVYTFemFzqrysWZgwnk+YSPPdZheGnafPL8x95Aj8X34Bz46f4N69C569u+HZtxcor4qw6HIh2L4Dyvv0Q3nPc1DetZv9IypFW+DUwByr936OZTsW49OdH0srXZGH8N0SK1x9C87FwFZDTdtWmKJmlJqtdztiKvc13dtOn7D0sTB9wtLHlvQJSw9b0ifMfjvaKsKemD5HInD3lLH2k0igBVpEmCj+zI6ZOHrEhc++KEW700JRa6w3+1VkzX4VGcuX6mpVqH42Ar37INCnP8p79UGg3wBUNjDH10dXQ1IwsVNE2JbDm7F89yf49KdF+HzXUpwMnqhFs1PjLhjSegQGtTkfYpthti87BWlb22SKMGv5JrN0irBk0ra2Loowa/kms3SKsGTStq4uijDr2Got2TYRli6BOQRorSLslkl+vD/Pg8f/EcC46yrq2Mj7/Rbk3vMbZHy+TPqtokUBSq64GsEzu6GiZWvAI172rDgCZfB/tRa+Navh/2IlxMpZ5BHsdAbKBgxC2YUXo2zQEISy6mkdG6dUOrtE2KHSg1i6YzGW7lwkfe47sacW9+b18jGo9fkY0maE9J/w6eIRmwBFWPqMEIqw9LElRVj62JIiLD1sSRFmvx0pwhK0gVafsPrZOTh+3IfiYwFkZTVAu/a1oyMOKguidO1qbOraFQPXrMEPoy5D99FjdEVHHNapKwq+/wFv7dyKCz5fgXaffoKXJ0/G8EWL0GbHDqmnCyffCM9p7dHtkitR0aYdGB0xPACUIkyvj4VaNMhow2rL9xuw9uvP8X3eNizd+TE2H/oWIdSsitbz1kf/ludhSJvhGNx6OMTKl/KIFx1Ry3CmT1htSoyOqGXUGEtDnzBj3PTk0jtf6SnbzLRmizAz5kIz+5duZdEnLN0sWrc/9Amz38a2iTDRdbEdsV3rfFw1arD9JAy2QI8IC4W82Le3HMXFDdGnrxceb1WI+hVLccGCBTiam4uN5/RCj3MHY8+xIwmHqM9v2Aj/faMQg3/aiQ4L5kOstH08YgQySktx3vLlKO/cBZtGXYqvWrfCBRNulggwRH0Z9N7UxBJhlaFKfPPzV1i28xN8umMRju85is6hzpiD8FZcj8uDs5qfg8Gth2Fwm2Hond8fXrcv6mg048aDIowizOB0pzsbRZhuZLoz6J2vdFdgUgaKMJNAJqkYirAkgbaxGoowG+FXVW2rCBMvbn5t7iLcd+s4ZGXWvFPKfizaW6BHhHk9XuzdF8DBnxuh0xleNGvuRuu9+7CipBgjFn+C/VePwQ8V5Za9J8y7bSvWfPAe6v3wPYbOmil18vtOnfBF7964dt48lA67EMcuuhgzjhzAxCl3VkPge8Jij4dIEba7eCeW7PgIn+74GJ/tXoKjpTXbRLuiK/p6+6GiswdDWg/Hea3P1xVMgyJsQtyTU+92RK6ExUVqOAFFmGF0mjNShDE6oubBoiMhRZgOWCmalCLMfsPZJsJiRUYUWNItOqJs6n884cOjf/Ni8s1B/O22rWg+4By4Sk7iyMuvoeSyK5M2IkSdGUsWI+Pjhchc+AE8e3bXqjvQpx/KLroEpRdchPIzuyetXXZVlIhP2LGyIizbtbjKt2sxdhzbVqsbIky8CBc/pO1wKahGy5zWdnXzlKhXrwg7JaCkaCfpE5aihlNpttkrYelDJvV6Qp+w1LOZWovpE2a/HW0TYfZ33bwWaA3MIWr8casLg/plIisLONR1ALLWrkDpxZfi8Cvh7Wl2Hb7Nm5CxaAEyPvoQ/tUr4Covr25KRctWKL1gJMouGoWyIecj5M+wq5mW1atXhO0/sRfv//gu5v/wHlbv+QwVoZpAK353BvoU9K+KYjgM3Zr2gNvltqztLLg2AYqw9BkRFGHpY0uKsPSxJUVYetiSIsx+O1KEmWADPSJMVDf2ygycvexfeAa/QWWTpjiw6mtUNmxoQkvMKcJ14jgyP/lYEmRipUx6N1nVEcrMkqIsCkFWetEoKYJjOhxaRNjO4p8w7/u5mL/1Xazbv6Y6oIYLLnRp0k3y6RrUZjj6FwxEpicrHbCkZB8owlLSbKqNpghLH1tShKWPLSnC0sOWFGH229FWEVZSGsCDj83A+x+vRIu8Jpj+6D0oyGsqfde/V9eUCNih1ycsUB5AqDQT+d+thrcyiKbnDcWqg/vQd8BQHC8uwratWyzzCRPDLXKft5boiP8ufA4jjxaj9UcL4F+zCqgIr/o8effduP7TZfBXibJAr76A2w21QBUVFRWY+fxTmHzrPbVGfcnJE3hndiHGT7496tnw7pxZGDj0QjRrnq+a5svVn0nxBXv1Haj6+8ED+7DskwW48hcTo9YRLTrid4c2Vq14vYtNhzZU58/wZGJgqyG48LRLEPysGOMn3Q6fP75fo7Dv1i0bMeLi0YbOfvqE0SdMz8B5/9+zcXbfASho2UZPNtPS0ifMNJRRC6JPGH3CrBhl9AmzgqqzyqRPmP32sFWEydERLx7WH49Nm43rrhqBDm0L8MW6zXhr3hI8dN9kxwfsMCLCGu3ahcxDB7GnsgDZgy/GoQPLHC3ClIE53MeOIWPxQmmVbHrrAtz4/PNocOyYNJIrGzdG6fAL8Y9uXTF+3CR4mjSpHuGpJMLmLZyN709+h7nF72Bb0Q/VfWic2QTD2l2EUR1GSyHk5dUuPSHqKcKMTXoH9u/FiqWLcMUYijA9BCnC9NAC9IwzfSVbl5oijCLMitFFEWYFVWeVSRFmvz1sE2HKlzWL1S+lCBNREx/712w8/Pub0Sg3x1JKytU4uaLCpx5An56dq+udO38p/vToDOnvS4b3ryUO9Yqw8uJjaLx9G9wVLnwSGARfvXZo2+bTlBFhSmO8XjgN13Q+C00+Wxb2JVuzWvr54d//Hvf8/e8I9eobfkn0iItQ2ukMR6+E7Sr+EfO3vY3CdbPQ5VgnHMVRrMRKaZuhWO264LRRODuvj+pYpAirwfLCs4/i5l/fb/o5q+fmWO92REZHNN1c1QVyJcw6tnLJFGEUYVaMMoowK6g6q0yKMPvt4UgRlsyVMCEGX579AW6dOFpadRN1T334BWlrpLwq9/j0OZj2yF2SIBSrd+K4e8rYauvp8QlrNuI8+NZ9iV1PzsJp901AZSXw5YZSNGte88Je+4eFsRa4jxxB5sdilewDZHyyCO7Dh6sLCrY9DWUXjJT8yAIDByGkYeuesVZoz3Ww5GfM/e4NvPf925KPl3yck98XV3Yai4tOu4yRDLXjdExKvSLMMQ1nQ+oQoE9Y+gwK+oSljy3pE5YetqRPmP12tE2Eia6LFaaVazdi6m+vwzMz/i1tR2zcMAe3PvAkxl421BafMDl0/j1TxkqrYZEvlBYiTSnKRD+0irCMz5ehyeUXoaKgJfZ//T1+e6sf77zlwZ33BnHfAzXRCO0fFua0wP/FKmmFTAgz3/qvqgsNZdVD2dBhKB15CUovvBiVzZqbU6GGUo6XH5cCawjx9fmupdVRDTs26owJPa7DRW3HoFWOPf4zGprPJBoIUIRpgJQiSSjCUsRQGppJEaYBUookoQhLEUPFaSZFmP12tFWEie4LUXPDnY/UIhG5HTCZmMRWyD88/AL+d+rNqkFClL+LlTI9Iiz3rttR/5WXceyhh3H89juwdo0bl4/MQKPGIazbWAqvN5k9TW5d7kMHkSmiLS6Yj8wlH8NVXFzdgLLzRyDQ71yUd++BwLnnobJBA1MbV14RwMc/LcDc72Zj0fYPUFZRKpWfX78AozuNwVVnXIueeT3QMNuPn4vKTK2bhSWfAEVY8plbVSNFmFVkk18uRVjymVtVI0WYVWSTWy5FWHJ5q9VmuwizH0FNC2T/MDkyo/z3mMuGVvuIRYowySfM40FlVcRAqTSXCwiF4PX5EAqFpN+ys3Pg/2k7Aj4fstt3gK9efbg9bsz7T1uc2XUJvL7h6H7WEWz9YQt69z0Xu3ftQO++A/DRh/Mw9pc3YPqzj+O2O+7HzJem4cprrkWD3IZ4tfB5jLr8ajRu3ASzX52B4RdegmbN8/DWG7MwaOhw5LdoiXfefBXnnjcEBS3DLwhesXwJfP4MqQ5xbN+2Fd+sW4vLrgxvrwyUleHlF/+JKbffXQ1GWbbSXi+/8E+MGTcB2Tm1RZNo66RbfgO/YsuhCMwh90FEV/StWgnvgg9QvmwJnh86BPf+/e/hol0uVHQ9E+XnDkTwvEEIDhqK2R+9jyHDLkJefgvV4bJ6xXIpXHy/cwdV/14ZqsTnu5fh7U1vYNV3n2FoYCiex/PIzWiIyztdiTFdfokBrQZBhJcXh9ftQv0sL4pOlGPZkkXIaZCLnueo+4BFNkKtv9HG9dbvv8N3m7/FqMuuMjT0y8vL8dJz/8CvfnOvofwik3J8GC4kSsZnnngYv7l7qtnFYv++Pfh08UcY+8voES7lSjN8bng9bpwoDWpqx/qv1qDo6BEMPv8CTen1JFow/z2c1r4jOnXuqiebaWn//dbr6NN/IFq1bmtamXoKUs5XevLJaetnehGsDKEsUPMePiPlaM2jZ5xpLdPqdHrnK6vbE638BvV9OFkaRLDCnK33ZsyFdrFIhXoj7xWUbW6c48eR4oAUlZhH6hJwu11oUM+Hv/z5ITz44IOp25EUbrmtIkxs9dt34HCtQBeRQihZbOV685s3rvb3UmuLmgjzeDwQIkM+XC6XJL58VSJM/Jbj9cK3dy/KcnKQ276DJFDcbjcOH26DQ4eWYMWKC3Db7Ufw44+b0f/cgdi54yecO2Ag3p/3H1x/w2Q8+fijuPf+qXhu2rO49trxyG3YEC8+/xyuvPoaNGnSFIUzXsTFl1yKvLx8vDKrEMOGj0DLlq3w2quzMGTIULRqHd5i9+mST5CR4ZfqEMfWrT/gq7VrcM3YcdLfZWVlmPbPp3Hn3fdV90dZttIe//rn0xg/4QY0iFi5Em29/Td31hFhch+UZZw4cQIvv/Ac7mieB/fCj+D+eBFcB/bXMvsLv/0tRjbIRYtWrVFx7gCEOtcETREJP1u+VGhenDdoMNbvX4c3NryGtzbOwZ7ju6Vy2nnaYaxvLHpf0g8XdbgYfk/dUPJCN/s8bgSClVi86CPk5DZAnz79NA0/tf5Gy/jdd5ux6dsNGH3VNZrKjkwkbjye+ccTuPve3xnKLzIpx4fhQqJk/L+H/4rfTf2j2cViz57d+PijhZgwcVLcssXTPXFxKQ9Wxk0rEqxZsxpFR45i+AUXakqvJ9F/3vs3OnbshC5dz9STzbS0b7z+CgYOHIw2be0RYcr5ykinvB4XKkNApfi/JBx6xlkSmqOpCr3zlaZCLUjk97olAVYpJmsTDjPmQhOakbZFRN4rKDua4fOgrDw5D0bSFrADOiYeQft9bvz5z3+mCLPJHraJMLVVJplBMgNziDrVBJjclng+YVqjI+aUBeA7VoTSZs2QnV8Any8swvJatMSqz5bjo48uwJDzD6NJ482Oe0+YMkS9cpyK6IiXXzNeWuVTHom+J8z37TfI+HQxMj75GP4Vn+HF6yfgkv/+FwV79kjViBdbB/qei/L+A1HWtx8WBI9i08ENePPEG/jhyBYpjdvllt7jJbYa9m8wEGuXLTX0njAt5yWjI9ZQYnTE2iNm8cJ5aNvudHTo1EXLUDI9DUPU60OqJwqnvpKtS83oiIyOaMXoYnREK6g6q0xGR7TfHraJMGWIetm3SsZhR4j6aC+HjgzEYSQ6ouvkCeR3agNXaQn2bdpeJxDF1+vduHh4BvLyQ/jPB2Vo1dqcJ4X2Dy9zWpDx2TL4v1gJ3+qVUhh89+FDdQpe0Rr4rDWwp3t7tBh5PS7qPQlNs5ppboDyZc2aMzGhIwnQJ8yRZjHUKPqEGcLmyEz0CXOkWQw1ij5hhrA5LhN9wuw3iW0izCkrYULwTbn/cezdX/vG/sZrR1VvS4z1njBhwnjREbPeeRONpkxCYMB5OPifhapWf+hPPjw/zYsuXSvx34VlyMy0f3A4rQUnyo/jwx/nYdXSl+BZsxL9dlTi3F3AWftd8ERsVwq2Px2Bfv1R3m8Ayvqei2CnM2J2hyLMadY23h6KMOPsnJaTIsxpFjHeHoow4+yclpMizGkWMdYeijBj3MzMZZsIE52IfCeX+E4WRbdNvMKWEPVG4MYTYY1/eTUyF36AokefwonJt6hWIVzKxozOwKoVbowcVYGXZgWMNCUt84iIhm9teg3/3Tq3un/NsprjstOvxlWdx+Gc3G7wf7kG/jVfwPdF1WrZzwdqsahs1AiBPlWiTIizc3oj5M+oTkMRlj5DhyIsfWxJEZY+tqQISx9bUoSlhy0pwuy3o60iTCm6lCtRdoao12uS+D5hlagMBtGgqAiuNu0QqAhKkfeUPmFrVy1H3wFDcejnY/hq7RZ8+ukgjLz4R4z5ZT8sWTQfo8dMwMznn8LkW+/B7FnTccnocVIZb732Ei4YNRoNGzWB0m/rvbdfRf/zhiEvvwDz5oroaIORX9BK6lrkPu8d27di44Z1GHnp1dLvgUAZ3ih8DhNvuaMaRbJ9wkTFO45twysbXsKbG2fh6tKr8F/8F0e9Rbi045W4otNYDG09orp9X67+TIrS1KtvONiIODw7tsP/xWppG+PhH7bggzM64pbp06t/D/l8KO9xdpUwOxeVA89Dg3YFUoh6vT4W9AmrOWvoE1Z7BqFPWM18pXduFemTLcLoE2bEStrymC3CguXleGXGs5g0hT5h2iygLxV9wvTxSsXU9Amz32q2izD7ESTWgngiDMFyVIRCyCkrgzu/AIHyQFQRdry4CFs2f4/33h2E1q2347Kr+qPo8LxTSoS9vfl1vLlpFj7fvbTaMHf770G7Xp1xac+rkeGpu09TTYQprXrwwD4sW/whxrU9HT6xWrZmFTJWr4Q7YrUsdHpHlJzTG4t69kDmOX3QrXc4jH+8gyKMIizaGKEIowiLN38k+rveh0aJ1mc0P0WYUXL25KMIs4d7MmulCEsmbfW6KMIStEFcEVZWhgq3C9luDzy5DeOKsG1bt6AiNABrVu3Cl1+dh9tv/zfGXJfeK2Fvvv4ivu+4HXO3zMaxsiLJIi2yW+IXnSfgum6TsXr+YgwceiGaNc9XtZYmEfbJgjrRET07f5K2MfpWrkDGmlXwfbVWKn/ByJHIPXoU/VeuROCc3ijvdhaC3c5Cec9zpL8jD4owijCKMHUCypV7I1MtV8LiU6MI40pY/FGiPwVFmH5mqZaDIsx+i9kqwkSExFsfeBLfbPqxDonuXdpj2iN3oVFu7fDn9iOr24JoPmHuI0eQ37GllGHfll2obNxYc/On3ufDrJe9aNkqhHffL0NBy/SKmChepvzBj+/h+a+ewZp9KyUuXrcXI9pdjF+eOQnnt7lQCjOfrEP2CSta+An8a7+Ab9UK+Nd9Cc/uXXWaUN61G8q7n4Vg9x7hLY1n9USofnaymsp64hCgT1j6DJFki7D0Iee8npi9Eua8Hp46LaJPWHrYmj5h9tvRVhGmFu7dfiT6WxBNhGXOn4fG1/8CgV59cHDBp7oLvuLiDKz5wo0WBSHMfieA0ztqe/ms7oqSmKE4UIzZmwrx4rp/YlfxDqnmljmtMbHbLRjbZTya1ctLYmtqqooWmMN96GBYlEnh8VfBv3YNXCUna7VRvLesvGt3hOrXR/mZ3VBxRleUn9EZ5Wf1tKUvp3qlFGHpMwIowtLHlhRh6WNLirD0sCVFmP12tE2ExXpPmP1Y9LUgmghr8Pv7kP38P1F83+9R/Ls/6isUwLEiFyb+0o/Vq9zIaRDCPfcHcfOvgrrLcUIGIbheWPcshmwUswAAIABJREFUZm8sxPHy41KTeuX3wy1n/wYXt78CHpfH1mbqiY7o27QRvi+/gG/9V/B/sQq+b9ZHbXuwQ0eUd+6CYJczERSfnTpDrKTxsI4ARZh1bJNdMkVYsolbVx9FmHVsk10yRViyiVtTH0WYNVz1lEoRpoeWStpYPmG+YBChUAgVPj/q5+TA6/Fq8gnr2as/9u7ZCfEpoiMuWnQjzur2KP761z/i/vv/gfOGXYtevXNSIjri6r2f4/l1z2DRj/Pxu9Dv8Ij7EYxqPxq/OudO9Gh+DkpOnsA7swsxfvLtUS3x7pxZlviEKStUijC9PhbCJ+yGfoNQ7/vv4dm0Ab7Nm+DbvBGenTuAUO1tpJu6dsU33bvjyq+/QbDzmQh26Yryzl2lz2Db0wB37C2YZkQEU0bPTHD418nO6Ii1kTAwBwNzmH2ORZand76yuj3RyjdbhJkxF9rFIhXqpU9YKlgpsTbSJywxfmbktk2EicaL7YjtWuenzPvA1IDHFGHl5VLo9Aq/H/WzjYswEaJ+xrSn8Mwzf8CECU9j1qyJuHpsNrp2fg4XXuLMEPUNBuXjxQ3PYv2BLyVsDf2NcEf5b3HZxPFS0A35SBcRdt2k2+Dz+2sNEbFtUayaeb/bBO/GbyVh9kNZCb5t1RJj58ypM5xCmVnSS6XDK2fdwgLtjC6oaN2mOq0ZNx4UYbXRb1i/FsXHjuLcQcPNmFNrlUERRhFm+qCKKJAijIE5rBhjFGFWUHVWmRRh9tvDVhEmXsz82txFuO/WccjKrH0Daz8abS2IKcICAYTcblT4fAmLMPGesGt+eS9efXk6/vnsRBw92hB33PlP9O53FYZd0NAR7wkrDhzDKxteBFaU4LHQYwgggLYN2uOms2/HmI6/xFsvvyi960x5pLMIUxtBIvrl1o1fY1ReS/g2fgvv5rBIE/8W/mdqR6he2Ncs2PEMlHQ9E8+FApgUwVHbaA2nogijCNMzXhJJy+iIidDTlpcijCJM20jRl4oiTB+vVExNEWa/1WwTYbEiIwosqR4dMevdt9HoputRetEoHH7tbVMtvX6dG/fe4cPGb8Nb1/JbhDB+YgXuurfc1Hq0Fra9aKu05XDOpldREgwHrehXcB5u6fkbXNT+Urjg0lqUben0+IRZ1UgRTdP37Tfwbv42vHL23Wb4Nn4DV3GxujjLyAxvYzytA4Knd0SwYycE258ufRfKqPs+Nava7bRy6RPmNIsYbw99woyzc1pOs7cjOq1/p1J76BOWHtamT5j9drRNhNnfdfNaoBaYI+fPf0TO009IATlEYA4rjnfmePFKoQdfrK7xIzqrRyWGDqvAiAsr0auPtdEUP9v1KZ5f9zQ+3v4hQgjB6/bhstOvkvy9ujXtYUWXLSvTCSIsWuc8e/fAKwTZpg2SOPP+sEVaOXOdCAc4UTsqClpKWxtFYBCxgiYCgvz/9s4EPKrq/vvfmexkBYSEEBaxCmJtsSiiKKKgolbxb13q0qoIotbWBeEFqq97sVDU9l/FiCC0VhH3FwWp0oLViqIWKwKCaAhb2EMWss7c9znnzp0tM5l7Z+4yyXzv8+SZ7Wz3c85M5jPnnt9pHXAMPGV9LGOYLAVTwpKlJxJvByUscYbJUgIlLFl6IvF2UMISZ5gMJVDCnO8FSpgJfRBJwrpf/lNkrfoHDr7wChrHXmRCLdGL2PqtG4v/5sZ7K9KwZXNAyAqLFJx/gQdnne3F6DFeGWEx0aPF04w3tizBvP/8LzYc+EoWV5TdFdedcBPG/+hWFOf2SrQKR/Ins4RFA+LetxfpW7cgY/M3SPvuW6SL9WffbUX691ujMhQzZGLD6eYzRso0SteucibNU9ILnrK+8Hbt6gh/MyulhJlJ09myKGHO8jezdkqYmTSdLYsS5ix/s2qnhJlFMv5yHJewtes24YY7Hws5g4VPTsMpQwbFf1Y25oy6JkzxIqOlBd6cHHi9XlPWhIn1VMFrLF7523yce2FoYI6GxhK8u/QFrFt3LpYv64drrnke778/GpWVfXHqcC/OO28lThqagVNHnCopVVZsxYb16zD2pz+Tj5ubm/DSwmdw/c13+Cm+/vIinHTG6Xhr92tY+OUz2NewV742xT0VXU/thauG/BLZaTn+9CJaYHigCo/HA7GujWvCNmPr5g0Yc8GlcY1SvYE5xMxZesV3yNj4NdK+3Yz0b7fIGTR3dTXmT5iA8999F2U72m5ELTadbu3TRwqZCAji7dMv8LisDzy9StttN6MjhuJhYA4G5ojrjW4gE9eEcU2YgeGiOynXhOlG1WETck2Y813nqIQJAZtTvgRzH7sLXQvzJQ0RrGPS1Dm47fpxHSJqYmQJE1MMCkSIem+2kDCPbRLWvUdxSOCFFxa8hIrKs7Hs7f7YVuHCmDEr0diYhQ8/PENu/nzysC048YTPMPCEK1Da24tepY0hElZVvwuvvrQAzzcuQBWqZB+d3nskJgy5HQdWb8cll1+HvDy177SDEhb9jS0Dc9ggYdFa4N6/D2+9/RpGZmSjbO9euCu3IX1HpQynn7ZjB1yNDTE/lUQofU+/fvD0LoNH3Be3Utr6YO7br2Li7VNjlmE0wd49u/HxB+9j3BW/iJnV6EwYoyPGRBp3AgbmiBud7oyUMEqY7sFiICElzACsDpqUEuZ8xzkmYQ2Nzbh/9gJccfGoNrNeQs5eWboKD04Zn/RRE9uVMK8X3swsRyVs6esv4pThI1FSWgZx2eI/3/sA2yqy8NabZ+LAAReOO24LTj55LV588Ro5GgsKmnD7r5/A+oobUHXsw/gUT+MW3II38SZGHX8eJp70awzqdoJM++LCuZQwAJGkM9pb22kJE+1qLzqiiNAohCxdSlkl3Nu3B0laJUTwkPaOBx94APc+Uy5n0YSYiVk1MZvmf9y/P0QofqMHJcwoMTX9O28sxknDTkdp78A2B/GVFF8uSlh83IzkooRRwoyMF71pKWF6SXXcdJQw5/vOMQkT0RGn/24eptz2cxzTL/QSJzEbNvvpxZg5Y6J/hsx5VNFbEL4mLH/WoxB/dXfcg5r7Hkrapn+31YVPP0nD1/914ev1bnzzjQvVDTXAyIeBU54GMnyzIp/dgrzP/y8GlRVj4PFeDBqsYNAgBYNP8KKoa+LrzJIBUEdcE+YENzFTll5RIQVNyJp7u5hJ2+GbSatE2p4qwNt+QBix7kzOnJX1QatYh9ZXEzbfJZDdj0ro1IzOhCVUGTNbSoBrwizFa2vhXBNmK25LK+OaMEvx2lY414TZhjpqRY5JWGeZCRNkwyWs2y+vQvaypTi04AU0XHKZ872sowVNnkbM/3Iu/rR2FmpbDsscR9dch9y1D6PiP/1QVxc5zHyPHooUs+MGKjh+sIKBg4SkeZGbq6PSJEpCCTOvM8RatLSdO5FWWYG0ym2qsO3cgbTKSrlOLdYhZso8ZWXwiPVoZX3g7SsufeyDppGjZACRWAclLBahjvM6Jazj9FWsllLCYhHqOK9TwjpOX7XXUkqY8/3omISJU3992QdYsnRVh14TFknCiocMRNqO7dj7+dcQ62eS/Xhxw/OY88mjEOu/xHF23/Nw34jfYWD3wf6m79juwjeb3PhmoxubNkHeikiMTU2Rz653mU/Ijvdi4CBIUROClpmke3JTwuwbpWlVu+X7I227EDQhZ2JmTX2cvmM7XHXRQ+9rrVTy8tSIjsW94C0ugaeX77a4FzL69EZ6WW8cyu8OJT90vaJ9Z8mazCBACTODYnKUQQlLjn4woxWUMDMoOl8GJcz5PnBUwsTpd8boiC5F7JoFpGdkQlGUpFkTJnl//AEyMjMxZOhwLNv6Jv76wbMoqy/Fi3gRP+75E/z21Efw7Yov20RHPOucsRBBP4IPsSbsxyf/AtsrC7FxgxubNghRc+GKy3+PP/xhMpqbA8aVnu7BtGkz8f4/ZqCgQMyaeXHcIAUDBtThv18swHXjfxX13fDmkr9gxKjz0KNnScQ0X3z6keQ9dNiIiK/v31uFf/1zBf7nquuj1hEsYUbXWHSmNWGJfiSZER1RRHCUs2dif7SK7+CurMTeQ/uxsrgHxr/6mpxV03soOV1UWSvpBW/PYvVW/AlxkxJXgi8P7UdNSxNOO3O03mJ1p2N0REZH1D1Y4kxo9PMqzmoSzma2hOmNFJtww1O0AK4J6/wdzzVhzvex4xLmPILEWhApMIeUMJcL6ekZSSlhuxt34Zl9f8aXe7/AcTgOIzPOwvAx5+CCY8ZFDVEfTcKiRUc85fTbsWVLFr7ZqM6gbdms4JqrH8Mjj9wbAjwvrx633DIXi1+ejD59FfTr50Xf/kDfvgr6ivv9FHy0ahElzEfNjC8e7QXmSOzdAJghYZHaEB6Yw33wINL27Ia7qkquQxOza27xt6cKGfvUx9hdBVdTY8xT+mT4cBzq1g3nrf1M7pPmLeyq3hYVwVvUTe6lJh4rRd18z4nXfGkKi4D09Kh1UMIoYTEHYIIJKGEMzJHgEIqYnRJmBdXkKpMS5nx/OCphj5cvQdXegyFRELW1YsOHDu6wIeqTVcKEdC15dwG+rdmMD/EheuX1xh3HTEGP6m4Ye/HlcjRG2yfMqIRF2ids4bNPYtiIKdi8yY1NGyHlbHtlAy65+Bn84Q/3RH03TJo0D1/+9wLk5vWSUhb+t3nDh5wJM/BZ0hkkrL3TDV4T5j58WMqZFLU9VVLS3Lt3+e8LWfusrDeqc7tg7LvvGqAYSCoujZRSpomZ775SVIR3uhXh6C55OLZniRQ6VezUtHZcKsnoiMa61EgUTmMlW5eaEkYJs2J0UcKsoJpcZVLCnO8PxySsswbm6HrzDch5fQkOPf0cGq5Uw747fXxXvQW///hBvLP1DYgLJYuyu+LXQ6fixh9NQlZattPNk+vKKrcJIXOhcptL7mdWWenC9m3qbW1N5KAgWsO7dlPkzJmYSevb34t+/aDOqvX3oqxMQXpG7FPkmrDYjDpKingCc4ioj+IySBGC33X4kLx1V6t/roMH4T6sviYfy+er4a4Wzx+OGQ0yKrf0dHgLCuHt2s03A1fkm3HzSZqcjfOJm+++EDspcMm6uNLkQcI1YSYDdbA4sy9HdPBUUr5qrgnrHEOAa8Kc70fHJKyzhqjvedoQpG/ZjL0ffYFWEZHCwWNP/W784ZNHsGTTX9HqbUWX9FxM+PGvcNvQycjP7DgBC6oP+aSsUgiaG5Xb4BM0N7Zvd6GlOTpktxso6aXNnonLG32XOvb3SnHrWazA5QIoYQ4OVJOrjkfCEmmCJmQuIWZi5u3QAVXYDlerAqfJnHjt4AHf42q4Go7EXa2IINnmkslCIXG+yyflbJt4rAYn8eYXBG7z8uKu1+6MlDC7iVtXHyXMOrZ2l0wJs5u4NfVRwqzhaqRUxySsM86EiS9VvfocBSUjA7t3HgKEAThwHG6qxv9+NgvP/7ccjZ4GpLszcO0JN+KuYTPQI6enAy2ytspdO11Sxior3NhWAd8smhvbtrmwp6r9WTTRsmN+4EX//gp+cIwbPUs96NvXi959FPTqpUoaj45FwG4Ji5eOq6VFnVWTwqbNvqkzbKq8VcMlZtvkrJtvZs4nd2htjbda+bnkzcuDkl8Ab34+lPxC3632uABKQZC0aRKXJ9IG0oi88hcMCw9KmIVwbS6aEmYzcAuro4RZCNfGoilhNsKOUpVjEibaIyIjTp85D+WzJvs3bBYbNU+aOge3XT+u464JA9ToiDYH5hg+6my8vmMJDn6yE+9438FO7MQ9OVMwauSFGHLsMDkEwq/zrqzYig3r12HsT38mX7dyTdiiZ5/E+FsnhwzFhiP1eG3xQsuiI4pZsg3r9+DLL1YAaePlLJp26aOQtMPVbb9Ejh27AtXVhVizZri8lLG4WBUyMaPWq1RBae/AffHcymVPIHwNXLS39vdbN2Pr5g0Yc8Glcb37GZjjFzG5GZWw9V9+jtqa6g4VHdFVW6teDum7hDJY4iCEzjcDt3hAP5y5/mv0/74C7toaiHzi0kuzDqVLLryRhE2IW14BnuvVA5d7XSjIzoGYvVOys9W/LHGbAyUnG9DuZ2f50oh0WRCRLe2WMK4JM2tktC3HbAkz47PQurPt+CVzTVjH78NYZ8A1YbEIWf+6oxImTk+Trt17DvjPduGT03DKEGcv5dOLPmJ0RAckbP7Cx/FS64vY2LgBEzABVT334TfnTMd3H6zHKcNHoqS0LCUlTJx0eyHqa2tdqPjehV073Ni3Ox0bvvEgI+197NlTiNWrh6PmcOxf+mfMmInn5t+Nrt0ypLD16KnI257FkDNp6nPq/f17v6GE6X1zBaUz8uU4FSRML8JogTnk2re6GriFlNX6bmsO+x7XwlVzWAqbu04VN03gAre1cNXH3s/tj3feiesXLkRRdbXeJrdJp4h1c9nZQASBC5Y57T58MoecLqrMCdkTopfjEz8pg1kRRXBPzSH8e82/MO6K2LIf9wmZnJGBORiYw+QhFfG7QnAdnAmzgrj9ZVLC7GceXqPjEuY8gsRa4LSEFZ5UjEe++C3OrR6NN/EmSorLcE3L1RhzzjgUl5Ri6esvUsIS2CdMBA0Rlzvu3uVG1W5x68JuEf1c3qqPJ9z0WJt90aKNqiFDNmLIkK+wYePlflkrLgF6+GRNiJqQuO7dlYhXs5rx628qRUfU8+7uiDNhes5LpLE6OqK7RkhaQOZcdaHCtqClAZcfrkVRfYOcgRNbBrgaGtVb8Tj4fmMTIJ4TQVJqavSeoqnpdpaVYfnYsbjphb+1ETgEy1zQTJ5fBLOzoIqfKnn+9EIec3wiqIlk8KyguJ/ApuKUMEqYqW8CX2GcCbOCanKVSQlzvj8oYSb0Qe2RFtQ2tKL7Jecj69//woG3VqBpxJkmlBy9iF11OzB91R14v2K5TNQ7vw8eOnM2xg64xNJ6O2vhiQTm8HiAA/td2LPHhb3ib696u6cK/vv7xOM9LhkJUs+RlgYc1UNBz57qujT5J2bYStTLI4Wo9SxRZ9lSJFCeHmwyjdGZMN0FM6HtBArdrfDUH0FDdZ1f4BBF4IIlT5M5V2Mj0OgTPnnru9/UBFeDJoa++6Lc2lrbzzG4QnF5Z8jsXZDA+WcCwwUuJwfyQ0Bc/p6RAWRmQBHXUWeot/K5jPSQ50R6JSM9kCcsnYy+GfxcVuJRdM2+HNHRjkrxyjkT1jkGANeEOd+PlDAT+kCTsOKfHI+0ym3Y88UGeMSOwxYdL21YiAf+NRV1LXXITsvBHcP+D34zdKpFtaVGsYlImBFC4vJGv6TtcWHfXoTImiZxIiKk3qOgULvkMfgySFXWtJk1cb+wKDWCjFDC9I6c5E9n95owjYjrSL1P2MIETmz+LUQuksAJ4TtyBC4heHJGLyB9Mo/2vMzrmw0U98XzOi7tTJbekqKYmREkaZr0BYlehpC8UPnLzMlCizsNnjSf/AWJniaEhmQyI1OKJtwuKOJXK3cakJam3vc9Vu+7A8/70ojLDELz+NJk5yQL5qRuByUsqbtHd+MoYbpRWZaQEmYCWk3CSo/qIkvbtT/+0NPtNUeEnL/7/UlYtf19meysvqPx+OhylOSWmnAWqV2EXRJmhLKI+Chm0AKza0BVlRA330ybnG3TL2ui7t5lYjZNQVGRKmVFRZD3CwqBwiKgsFB7Tb0v0uTmGmm182kpYc73gVktcErCzGq/0XJcdXVtBM4vc/JSTlXg5GygJnAi0IqQutYWoKXVd9sCEX0TreK2Vb1tbgZERE6RrtUDV0uzmkZ7rtn3mngclFcIaSof4nJTKXVpbigi4nGI4PnET5M7kSZICKUUtsnjEz5/Hp84BpdhtJ70dH+7/IKpyWeUehTf6/K6d3eQvMo2p6mCKw7xL8blgiIiofr+uhdk42Btc8hz8jyD0rS5LwoKK0dNo5Yf/Oevy5dHvhZWfnB71CitoWWE1hWhDhNmdzv6+4IS5nwPUsIS7INIa8LUTxXF1OiIC8rn4PGMJzC+6Ua8mvka7h55L9yfN+PcCy9FUdfueP3lRTjrnLHo3qMYwWt+uCas/cAcWvcHS5jRNRYLy590NDri/v2hYibErUpcCilm2vapoibErd73XWrChPl4993zsWOHGqxFzyHWqAlRExtjF+QLORPSpqjS1tWl3i9QsHPbTAw7Yxry8xWIZS75BYq4iirhg4E54kNo9ZqwWK1a/JdyXHTpz5EvBk8ch90SZmScxXE6lmQx+nmVSCNkZE0hepq4+W/V58SmjX6Ba/WIcLt+KSzIBBpqG+BpCpM/X3lCFGV6EdJWh0y2Kl78acRpuOfvKwGvB/B44PJ65a16X72FxwuXuPU/9gQee32viTQJ7NuXCNNkzbtyzBhkNTbijA8/TNYmOtYuKeZthDNMVjVpDJPDNvIYSVwRKr2BunwyKWZytXwR5DOi0AbXo+Vxu5CRnoaHxozG/fff7xjPVK6YEpZg71stYSv//v/wdu4ynLb9ZDyCRzAtfTouuexa9Os5AK/8bT4lDMAXn34ktwQYOmxExN5sLzpiZ5AwvUO4oQEyuMi/P3gB+YWj0dhUhsPV8P25UH1Y3FfD9h8+DFRXu2R0SL3r2EQ7HnjgQTzwQNsP86KuqpTl5akyl5vreyxlTTznkq/lCXHTbvN9j/MVNDXuwrrP3tcVtc7oTBgDc+gdQcbTUcKMMzOaw04JM9q24PRmrwkzI0iRnvORcqaJnE/mgmVPyJ2UPI8qgAH5055XBVDm8SqQe/z58/iEMUgSXb5y/Gk0sQzJEyaWokytbfJWidwWTVaD2htej9b+1UcfjcyWZpz+XQWgKIE/KMhMc6G5RdTjhSv4tUj3xX9nRYmQTvxWHVSulsaXXr4mzj1SmrD2RE8ToQ5xSTGPEAIPPvAAJcyhMUEJSxC8lRJW3aMW33y8DuVKOaZhGkrPPxYNHx/0/7JMCVM7jxJmbBDHEx1RzKoJKRNy5he1GvV+9SH4nz99+CN45dX7UFvjQm0dcOigscslo51JWdlOjB27HC8vuUmVuXwFRYVAly4BUZMCl6+gezc3iorcSMts8afNz1PziLxiDV3wQQkzNn6MpKaEGaEVX1pKGKMjxjdy2s/F6Iht+YioruHCJ38B1gQyWBqDZTKihIYKqNxdNmo6+IXUL71h5ceUVSGuYXnSABTmpuPh1aspYVa8iXSUSQnTASlWErEmTJk9GwUP/BZ1t/4aNQ//PlaWdl+vbjyEu1bejL9//45MN+7YK/DIWY+jW3b3hMpl5ugEknFNWGfpL7EURezHVlcbfuuCCEZXV+tCTY2CurrAY+15kU+7L2byzDjEVRliJk6TtpDboFm4/AKXlDpN3kJu81SZE1ec8LCOgN2XI1p3JizZ7JkwEnWOAANzOMfezJq5JsxMmvGVRQmLj1tILiFh7jt+g9znnsHhR2ah/pbb4y5ViNc9K2/Fgcb9OCqnBx4fU47R/cbGXR4z6iNACdPHyelUImpkjU/cAqKmipwQtvo6BUfq3Kivd+PAIW9E8dPWxplxLmK9mypq2m3wZZZqcJPsHJecsRORxNU/RWwnJW9FMDb5nP/1jhcIxQyO0cqghFlJ196yKWH28rayNkqYlXTtK5sSZh/raDVRwkzoAyFhGZdfhuzlb+Pg8y+i8eJLDZe690gVZqy+C8u3viXzXj7oGjx85hwUZMW3oN1wA1I8AyWs8wwAPWvC5OWSQTLX0CAut4R6GaWYsatpO3t35Ii6bk4VPjWtlYcIdhJJ3KI91yXXFSJ4Il2XLkBGpoKsTCAzSw14lpmlPhYRvkWUcLEWL1kPSliy9ozxdlHCjDNL1hyUsGTtGWPtooQZ42VFakpYglTNWBP22Sf/wmr3amS2ZuIE1wkYcOJg5DfkYsjQ4Vj1/jJcesUvsOjZJzH+1skIXmPBNWFq53FNmLFBHM+aML01zPvzLEy83fw964xErdMjYcHnk8iaMDGrps3ChVxuWadeftnc8BbqjhyLw9UnQFxOKWRPvQUajgTd154/4hLRxk07brhhEVatOgsVFfr2LRRCJsRMCJoqbopP3NTHQujE61lBQhf+WM3nQmamgjTlaWTlXoPs7CJZltheSsigyNPmsa9s+bpPFnt2y0CrR0F9Y6tpTNoryMg4s6VBOirhmjCuCdMxTAwn4Zoww8g6XAZNwh55+CGuCXOo9yhhCYJPVMLqcxqwb+MOvIf30CerH36S/hMMPXkEdu/aTgnz9c2bS/6CEaPOQ4+eJRF7ixJmbBBTwkJ5JSJhscj/4+9L0a//D3DMccfHShryul/YjkQTNxdEtHBN5o4cUSIK3gmD/4pNm0aiqqo/mpqB5iaXiAIe+GtSRdCq4847/4iFC69HdXVRQlWIGT0pbb7ZO/U26HGY4AXP/gWnzcp2SanM8pWlzQZmZSpSPL2eXdhX9R6OHfxLbWsouQewtm2T2FpJ3XZJ0baLEnsFq2m1/YL9W0mpaczYoqE9eJQwSlhCb64omSlhVlBNrjIpYc73ByUswT5QJcwNr4iK4z/07RMmLkFcvv9tnI2zsT53Ay7rfxV2b6uU8kUJC9CkhAVYmBGWmRKW/BKW4MeSP7uRfcLEDFxLs8sna3IPXzT5pE1s3STkLfixlLpml9gayi94Ik9zk4LGJrWs4qOewrbt16L+SJF8rJahlt1GCH2vS0lsCuxrZxYLPeVoUTife26CnuQJpRGXi6r75KqyFhA8/97AcPmETkiflL/AXsGqGLqBH/7w72hsLMT2HcPU8nx75mr3RdmiHPnYt+etTOP2iaTveX8aLW2bWyWkHLE/sMvt8tepla2WEyhb22e3IDcdTS0eKFDLkeertdetBrnxt9Envv7n2pyTKKUFG9b9CUNOmRxUjk+G25xTUPlh5xXMJsAqkF7M+qbiQQnr/L1OCXO+jylhJvRB/br1yD3pRHiOHoA9a9frKvGpz+fgdx/41TKfAAAaEElEQVTfJ9OO6X8Bnr3gb8hKM2FXW121M1E4Aa4J6zxjwujliJ3nzDvfmWhrwqr2eXzips3i+Wb0moDmSELX5PJJpC+9kEkplYoUPFUw1dfCxbOlxQWP2HbJt++vtsev3ObJvxewS937V0sjXgt+LLd/snaWsfP1dsc7IyFoflEUohwmu8FiKwUvSIKFqKoyHC6kQWVq6aWUBsoPLqc9ydZmcIUgxyPZokeEaIfvJ1zQJR11Da3+58Xev6r8K233MBa/SYv6ffsMR9qbOOq+w0F5ZCRaUU6UOoLLj7F/sWxjcJu0Hy4CbVPPo005Ec4hWl2yTF/6tmnacvKnicEpwDoy00BdbesI/0GBa8Kc/8yhhJnQB0eWLkeXSy5E84iR2P/Wu+2WKH6/m7HqTvxl/TyZ7qYf/QoPjpwFl3y78nCKACXMKfLm10sJM5+pUyV21sAcYtZR3VvXpYpdmPCJx0LqVOkLFT7/vr4+KVQlUS1H26YoWBgVLZ1v71uZxhuoV32s5g3+E9sKybrk865AGl85nlYlkF7bV9eXVpNVbb9d8TgzPQ1NzV60tiryfP3t9bVF28tY3vrrjXRObdsSfA7aXsWBcwqwaXOO4WxkvYH0Rjaqd+o9wnpJIFECU6a3Ytbv0hMthvnjIEAJiwNaeJbGZ+Yh+9abceSqa1H9lCpXkY5WbwtuXn4tVnz/tpSuWef8GdcMvtGEFrCIRAlQwhIlmDz5KWHJ0xeJtqSzSliiXDpi/s4WHVEIWkDqVFEOFslgsRXSGSq6qujJ54JkNySNJs1Bgh0u2SHCaoFkC4lu8wegS2YG6hpagl5ztU2n7Q2s7mXc7l/wHsKCR3h69fXIdfj2SpZ5YuxfLHkHpw+tJ1B+m3IinEOkuvx7NfvSt03T9hxkGh2MZNs1Nu22p20dsX5MoIQ594lKCUuQvVgTJnYd94SUE3lN2J6GKnhbPahGNY7rcTx65BajuFdvfP7Jhxh2+ijU1R7G91s3c01YWJ9wTVgACNeE/SLmO9aohCVjYI6YJ6kzgZE1YTqLNJQsOJqroYy+xHZLGKMjxtNL+vKYLWFmfBbqa3lqpuKasM7f71wT5nwfU8IS7AMpYYoCj7yAWDvaSlhTWjNqWg8jx5WD4m6lKMrtJgN6UMLq8drihbhu/K+i9gQljBJm5MsxJSwwXihhxj7gjYwzYyVbl5rRERkd0YrRRQmzgmpylUkJc74/KGEJ9oEeCfN4W1GtVENxKSjO7oWuRd2RkZFJCYPYK4kSZmQImvHrL6MjhhLnTJiREWgsLWfCjPGKJzUljBIWz7iJlYcSFotQx3+dEuZ8H1LCTOgD73ED4d6yGXs/+hytA0P3A/pwxypc/dZPZS0vjXsbZ5SNMqFGFmE2Aa4JM5uoc+UZnQlzrqWsORYBuy9HjNUevh4/AbMvR4y/JcyZKIFe3XJQdbBBrmXi0XEJMDqi831HCTOjD8Tun62t2L3jAJTsHH+JlTXf47zFp6G2uQbTT3sItw+9x4zaWIYFBChhFkB1qEhKmEPgLaiWEmYBVIeKpIQ5BN6CailhFkB1oEhKmAPQw6qkhCXaB/v2AT17Qikswu6tu/yl1bfU4YKXR2Br9RaMHXAx5l/4cqI1Mb+FBChhFsK1uWhKmM3ALayOEmYhXJuLpoTZDNzC6ihhFsK1sWhKmI2wo1RFCUuwD+SaMI8HHrFjov9QA3M0oxlpSEO6Kx25eflIT0tHc0sz8gsKuSbMx4prwowNQK4JY3REIyOGgTmM0AIYmMMYLyOpzZYwMz4LjbQ/1dJyTVjn73GuCXO+jylhCfZBZAkTCqagFa3ISsuG4vVSwjweLHr2SYy/dXIIcUqYsQFoxhcPBuYIZc7AHMbGoJHUDMxhhFZ8aRmYg4E54hs57eeihFlBNbnKpIQ53x+UsAT7IJKECQETR1p6OlyK2JTRQwmjhMkxIfaB27p5A8ZccGlcI48SxpkwIwOHM2FGaHEmzBgtY6k5E2aMl9OpKWFO94D19VPCrGccqwZKWCxCsV6/5x5gzhzU3Psg6u6cgtMWDUZlbQXuP+Mx3DzkN7Fy8/UkIcA1YUnSESY0g2vCTICYJEVwTViSdIQJzTBbwkxoEouIkwDXhMUJLsmycU2Y8x1CCUu0D666CliyBIeeWYA5A3bh0X/fi+O6HY+VV6+F2+VOtHTmt4kAJcwm0DZUQwmzAbJNVVDCbAJtQzWUMBsg21QFJcwm0BZXQwmzGLCO4ilhOiC1m+S004A1a7D1tVdx0jc3ora5Fq/+zwqc1vvMREtmfhsJUMJshG1xVZQwiwHbWDwlzEbYFldFCbMYsI3FU8JshG1hVZQwC+HqLJoSphNUtGTtRUdMT8+AoihcEwbAwzVhcghxTVh8bzgjUeuMShgDc8TXJ3pyMTCHHkqJpWFgDgbmSGwERc7NNWFWUE2uMrkmzPn+oITp6IPXl32A+2YtkCkvGj0cD04Zj5zsTPmYEnYd8vLyQyguLH8S1954GzIyVUbioISpHChhOt5wEZJQwuLjxsAcxrgZGWfGSrYuNSWMEmbF6KKEWUE1ucqkhDnfH5SwGH2wdt0mzClfgrmP3YWuhfl4vHyJzHH3pCv9Eub2euB1t90njDNhlLDw4UUJi+9Dz8iXY86EBRhTwoyNNyPjzFjJ1qWmhFHCrBhdlDArqCZXmZQw5/uDEhajD4R09e9TgssuHClThksZXC6sKQPOuaUL1ly/EUfl9HC+V9kCwwS4JswwsqTNYFTCkvZE2DBwTVjnGQRcE9Z5+pJrwjpHX3JNmPP9SAlrpw8aGptx/+wFGD50sF/Ctm7bhd/OnIdHp0/EMf1KISRsyQnAuscfwu1D73G+R9mCuAhQwuLClpSZKGFJ2S1xNYoSFhe2pMxECUvKbomrUZSwuLAlXSZKmPNdQgnTIWFXXDwKpwwZJFNGkrBnRuXhhvf2ITs92/keZQtIgARIgARIgARIgARIgASSmgAlTIeEtTcTJgJzuNwuKF7FX5LL5ZJRETMy1OiIIihFQUEB0tPT0dzcjKKiImRmZsLtdqNv37745z//iXPPPRfV1dXYuHEjzjzzTFRUVMjbN954AxMnTsTMmTNx77334o9//COuv/56WcZTTz2Fq666CkcddRTKy8sxbtw4lJSUYP78+Tj//PNRVlaG559/HqNHj5b1iGPlypXIysrCGWecIR9v2bIFa9euxTXXXCMfNzU14YknnsC0adP85xNcdjAuke6mm26S5xZ8iLZOnjxZnqN2CAbaOQSnra+vx9y5c3GP2PQ6yjFv3jxcdNFFKC0tjZhi9erVkvOoUaMivr57924sXboUN998s64344oVK1BYWIjhw4frSh/pfKNlFP371Vdf4cor1TWFRo+WlhbMnj0bM2bMMJrVnz54fMRdSJSM4v1w//33m10sdu7cieXLl2PChAmml/3JJ5/g0KFDGDt2rOllv/baaxg4cCB++MMfml62ngIXLVqEs846C/3799eT3PQ0wZ9XphduQYFWjjMLmiuLNPp5ZVU77C7XjM9Cu9vckeoL/67QkdrOthojYNX/bWOtSM3UlLAY/R5rTZgYvG53mgxDHzhcABQwMAcDc4QPLwbmiO+D1kjABKOXIzJEfXx9oicXQ9TroZRYGgbmYGCOxEZQ5NwMzGEF1eQqk4E5nO8PSliMPtAVHZESFkKRIeqjDypKWHwfepSw+LgxOqIxbkbGmbGSrUtNCaOEWTG6KGFWUE2uMilhzvcHJUxHH7S3T5jIXnukBbUNrTpKYpJkJcDAHMnaM8bbZXQmzHgNzGEXAQbmsIu09fUwMIf1jO2qgYE57CJtbT0MzGEtXz2lU8L0UIqRhhJmAkSHi6CEOdwBJlZPCTMRpsNFUcIc7gATq6eEmQjT4aIoYQ53gEnVU8JMAplAMZSwBOBpWSlhJkB0uAhKmMMdYGL1lDATYTpcFCXM4Q4wsXpKmIkwHS6KEuZwB5hUPSXMJJAJFEMJSwCeyMrAHNchLy8/hCLXhEUfVFwTFt8bzshaHaMSxsAc8fWJnlwMzKGHUmJpuCaMa8ISG0GRc3NNmBVUk6tMrglzvj8oYQn2ASWMEhZJOqMNK0pYfG84Slh83BiYwxg3I+PMWMnWpaaEUcKsGF2UMCuoJleZlDDn+4MSlmAfUMIoYZSwwJto3p9nYeLtUxN8V7XNbuTLMWfCAvwoYcaGopFxZqxk61JTwihhVowuSpgVVJOrTEqY8/1BCXO+D9gCEiABEiABEiABEiABEiCBFCJACUuhzuapkgAJkAAJkAAJkAAJkAAJOE+AEuZ8H7AFJEACJEACJEACJEACJEACKUSAEpZCnc1TJQESIAESIAESIAESIAEScJ4AJSzOPjh0uBa3TnsCX238Tpaw8MlpOGXIoDhLYzYrCBjto/bSb922C5OmzsHuPQf8TT3x+AGY+9hd6FoYGqLfinNhmaEEXl/2Ae6btUA+edHo4XhwynjkZGe2i0n04eynF2PmjInsMwcHlJl9F1yWdko3XX0h7p50pYNnmJpVNzQ24/7ZC/DOyjUSwMNTx+OyC0dGhfF4+RLMf2mZ//VY6VOTqj1nbWbfhf8fFWfQq7g7ymdNxjH9Su05IdbiJ7B23SbccOdj8nGs7yzhfRcrPTEnToASFgdD7QNr+NDB8p+M+HL325nz8Oj0ifyQiYOnFVmM9lGs9OxjK3opvjLFP5U55Uv8Aiy+zIkj2hfv4H8s/KcSH3Ozcpndd0LC1ny+QZeEm3UOLCcygeD3ofaemzzpyog/TorP27mL3sSNP79A/iCi/cg1c/pE/pjpwAAzs+9i9b0Dp5eyVYZ/b4n1eSk+n7fv2uv/8SRW+pQFa+KJU8LigBn+i3r4F/g4imQWkwkY7aNY6SlhJndQAsWJLwz9+5T4/1GEf7GPVjRnwhKAblJWs/uOXxJM6pgEixFfvKf/bh6m3PZz/w+RsX4cCa6S/0MT7IAEspvdd5SwBDrD5Kzi87Fie5X/B0qj32P0/m81udkpVRwlLI7ujjQwjfzDiaNKZjFIwGgfxUoffjkiZ1QMdohJySN9WdP7j4USZlInxFmMFX0XfjkiL0WMs3MSzBbpPWhEkPnFPcEOSCC72X0XfkkbL0VMoHMSzBr+vdTo+0zkr9p7kFcaJNgP7WWnhMUBV3xhf2XpqpCBSQmLA6SFWYz2kdH0/HCysPPaKVr7In/FxaP8ly1RwpzpC6O1Wt132heMKy8e1e5aJKPtZvrYBCL9wGFEwvj/MzZjq1JY3XdiHCxZuorrp63qwHbKDb/yQK+EaT9u8cdm6zuNEhYH41izJnEUySwmEzDaR0bTc1bF5A7TWZwVsyk6q2ayBAnY0Xfhl98k2GRm10kgkdkU/qClE7JFyazuu0iXO1p0Kiw2jECiM2G8HNH6IUUJi4NxrPVDcRTJLCYTMNpHiaY3ufkszsCve3r/UVCcnR9WZq8JCz8jSpgzfRzvuiIKmDP9FVyr1X1HCXOujxNdE8a+s77vKGFxMI4VSS+OIpnFZAKx+ig8Gles9CtWfYofHF0W16Jzk08t5YuLFWEv2uUvlDDnh46ZfSfes6+9sxo/u+gsuT2B3kttnKfQOVvQXoS9SJeK8hLE5BkHZvadeI+LQ9uyx8hlqclDpHO0JFZ0xPDvQaKv+pT2DOk7Xkpq7VighMXJ1+geVHFWw2wJENCz71dwSOT20gfvtSGapHdvqgSaz6ztEGhvr6lwCYu0bw0DODg3vMzsO+415Vw/htfc3l5T4RIW6T3Jz1Xn+tLMvtu1Z3/InppcV+Rcv4qa29snLFzCGIDM/r6ihNnPnDWSAAmQAAmQAAmQAAmQAAmkMAFKWAp3Pk+dBEiABEiABEiABEiABEjAfgKUMPuZs0YSIAESIAESIAESIAESIIEUJkAJS+HO56mTAAmQAAmQAAmQAAmQAAnYT4ASZj9z1kgCJEACJEACJEACJEACJJDCBChhKdz5PHUSIAESIAESIAESIAESIAH7CVDC7GfOGkmABEiABEiABEiABEiABFKYACUshTufp04CJEACJEACJEACJEACJGA/AUqY/cxZIwmQAAmQAAmQAAmQAAmQQAoToISlcOfz1EmABEiABEiABEiABEiABOwnQAmznzlrJAESIAESIAESIAESIAESSGEClLAU7nyeOgm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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_history(colors=[\"blue\", \"green\", \"red\"],\n", " title=\"Coupled reactions A <-> B and A <-> S (fast but disadvantaged energetically)\",\n", " show_intervals=True)" ] }, { "cell_type": "markdown", "id": "f4a147c6-cad1-47ca-bc1e-79b43a29e5c0", "metadata": {}, "source": [ "### Notice how the \"alternate (shunt) path\" of the reaction, i.e. S (red) \n", "### has a FAST START (fast kinetics),\n", "### but EVENTUALLY PETERS OUT (energy dis-advantage)" ] }, { "cell_type": "code", "execution_count": 17, "id": "104ccbd8-d2d8-475e-a9e5-40698293a077", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "From time 0 to 0.0005, in 2 steps of 0.00025\n", "From time 0.0005 to 0.00225, in 14 steps of 0.000125\n", "From time 0.00225 to 0.00295, in 4 steps of 0.000175\n", "From time 0.00295 to 0.00393, in 4 steps of 0.000245\n", "From time 0.00393 to 0.005302, in 4 steps of 0.000343\n", "From time 0.005302 to 0.006743, in 3 steps of 0.00048\n", "From time 0.006743 to 0.009432, in 4 steps of 0.000672\n", "From time 0.009432 to 0.01226, in 3 steps of 0.000941\n", "From time 0.01226 to 0.01753, in 4 steps of 0.00132\n", "From time 0.01753 to 0.0249, in 4 steps of 0.00184\n", "From time 0.0249 to 0.03524, in 4 steps of 0.00258\n", "From time 0.03524 to 0.04608, in 3 steps of 0.00362\n", "From time 0.04608 to 0.06127, in 3 steps of 0.00506\n", "From time 0.06127 to 0.07544, in 2 steps of 0.00709\n", "From time 0.07544 to 0.1151, in 4 steps of 0.00992\n", "From time 0.1151 to 0.1429, in 2 steps of 0.0139\n", "From time 0.1429 to 0.1818, in 2 steps of 0.0194\n", "From time 0.1818 to 0.209, in 1 step of 0.0272\n", "From time 0.209 to 0.2471, in 1 step of 0.0381\n", "From time 0.2471 to 0.3005, in 1 step of 0.0534\n", "(69 steps total)\n" ] } ], "source": [ "dynamics.explain_time_advance()" ] }, { "cell_type": "code", "execution_count": 18, "id": "bd33b1e8-abd2-4392-9884-8fd56ee0841c", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABScaption
00.00000050.0000000.0000000.000000Initial state
10.00025047.7500000.3750001.8750001st reaction step
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650.1623546.59394033.31505810.091002
660.1818006.37549033.9226089.701902
670.2090246.16354834.5120629.324390
680.2471385.99434934.9826249.023027
690.3004985.90006135.2450138.854926last reaction step
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70 rows × 5 columns

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" ], "text/plain": [ " SYSTEM TIME A B S caption\n", "0 0.000000 50.000000 0.000000 0.000000 Initial state\n", "1 0.000250 47.750000 0.375000 1.875000 1st reaction step\n", "2 0.000500 45.648594 0.732656 3.618750 \n", "3 0.000625 44.667193 0.903381 4.429427 \n", "4 0.000750 43.718113 1.070318 5.211569 \n", ".. ... ... ... ... ...\n", "65 0.162354 6.593940 33.315058 10.091002 \n", "66 0.181800 6.375490 33.922608 9.701902 \n", "67 0.209024 6.163548 34.512062 9.324390 \n", "68 0.247138 5.994349 34.982624 9.023027 \n", "69 0.300498 5.900061 35.245013 8.854926 last reaction step\n", "\n", "[70 rows x 5 columns]" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history()" ] }, { "cell_type": "code", "execution_count": 19, "id": "b139f5e4-625f-4a5e-8f57-8f00244dced4", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: A <-> B\n", "Final concentrations: [A] = 5.9 ; [B] = 35.25\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 5.97367\n", " Formula used: [B] / [A]\n", "2. Ratio of forward/reverse reaction rates: 6.0\n", "Discrepancy between the two values: 0.4388 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n", "1: A <-> S\n", "Final concentrations: [A] = 5.9 ; [S] = 8.855\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 1.50082\n", " Formula used: [S] / [A]\n", "2. Ratio of forward/reverse reaction rates: 1.5\n", "Discrepancy between the two values: 0.05463 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that all the reactions have reached equilibrium\n", "dynamics.is_in_equilibrium()" ] }, { "cell_type": "code", "execution_count": null, "id": "f87fe3c7-2c0d-4e3c-aff0-350bd04ea1a7", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "9e9260a7-5777-4eee-93b8-c46b8364e24f", "metadata": {}, "source": [ "# Scenario 3: \n", "### downregulated by shunt: \n", "### kinetically slow, \n", "### but with thermodynamical advantage (i.e. energetically favored)" ] }, { "cell_type": "code", "execution_count": 20, "id": "04476dab-f845-4533-8f26-fd0eecf8304f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 2 (at temp. 25 C)\n", "0: A <-> B (kF = 30 / kR = 5 / delta_G = -4,441.7 / K = 6) | 1st order in all reactants & products\n", "1: A <-> S (kF = 3 / kR = 0.1 / delta_G = -8,431.4 / K = 30) | 1st order in all reactants & products\n", "Set of chemicals involved in the above reactions: {'B', 'S', 'A'}\n" ] } ], "source": [ "# Specify the chemicals (notice that we're starting with new objects)\n", "chem_data = chem(names=[\"A\", \"B\", \"S\"])\n", "\n", "# Reaction A <-> B (as before)\n", "chem_data.add_reaction(reactants=[\"A\"], products=[\"B\"],\n", " forward_rate=30., reverse_rate=5.) \n", "\n", "# Reaction A <-> S (slow shunt, excellent thermodynamical energetic advantage)\n", "chem_data.add_reaction(reactants=[\"A\"], products=[\"S\"],\n", " forward_rate=3., reverse_rate=0.1)\n", "\n", "chem_data.describe_reactions()" ] }, { "cell_type": "markdown", "id": "6154b260-ce64-450a-b069-22cb920818d3", "metadata": {}, "source": [ "### Set the initial concentrations of all the chemicals, in their index order" ] }, { "cell_type": "code", "execution_count": 21, "id": "a45c9ebf-d06e-443f-a1a1-a5b2db6803b7", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "3 species:\n", " Species 0 (A). Conc: 50.0\n", " Species 1 (B). Conc: 0.0\n", " Species 2 (S). Conc: 0.0\n", "Set of chemicals involved in reactions: {'B', 'S', 'A'}\n" ] } ], "source": [ "dynamics = ReactionDynamics(chem_data=chem_data)\n", "dynamics.set_conc([50., 0, 0.], snapshot=True)\n", "dynamics.describe_state()" ] }, { "cell_type": "markdown", "id": "e6bddc07-e9cf-4236-bd2b-0e1fe0567800", "metadata": { "tags": [] }, "source": [ "### Run the reaction" ] }, { "cell_type": "code", "execution_count": 22, "id": "3800cb7b-475e-4437-a982-af2760355795", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* INFO: the tentative time step (0.005) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.25 (set to 0.00125) [Step started at t=0, and will rewind there]\n", "454 total step(s) taken\n" ] } ], "source": [ "dynamics.set_diagnostics() # To save diagnostic information about the call to single_compartment_react()\n", "\n", "# These settings can be tweaked to make the time resolution finer or coarser\n", "dynamics.set_thresholds(norm=\"norm_A\", low=2.0, high=5.0, abort=10.0)\n", "dynamics.set_thresholds(norm=\"norm_B\", low=0.008, high=0.5, abort=2.0) # The \"low\" value here seems especially critical to fend off instabilities\n", "dynamics.set_step_factors(upshift=1.5, downshift=0.25, abort=0.25)\n", "dynamics.set_error_step_factor(0.2)\n", "\n", "# The changes of concentrations vary very rapidly early on; automated variable timesteps will take care of that\n", "dynamics.single_compartment_react(initial_step=0.005, reaction_duration=7.0,\n", " snapshots={\"initial_caption\": \"1st reaction step\",\n", " \"final_caption\": \"last reaction step\"},\n", " variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "code", "execution_count": 23, "id": "8a533692-7830-49a2-83f5-8da6aa201935", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=A
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_history(colors=[\"blue\", \"green\", \"red\"],\n", " title=\"Coupled reactions A <-> B and A <-> S (slow but with energetic advantage)\")" ] }, { "cell_type": "markdown", "id": "05dbe681-2fa9-478c-b4eb-8c322e173c0c", "metadata": {}, "source": [ "### Notice how the \"alternate (shunt) path\" of the reaction, i.e. S (red) \n", "### has a SLOW START (slow kinetics),\n", "### but EVENTUALLY DOMINATES (energy advantage)" ] }, { "cell_type": "code", "execution_count": 24, "id": "f0d7d7ed-158c-4cf4-8d95-ef057ca612d6", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "From time 0 to 0.0025, in 2 steps of 0.00125\n", "From time 0.0025 to 0.03281, in 97 steps of 0.000313\n", "From time 0.03281 to 0.05859, in 55 steps of 0.000469\n", "From time 0.05859 to 0.07617, in 25 steps of 0.000703\n", "From time 0.07617 to 0.09199, in 15 steps of 0.00105\n", "From time 0.09199 to 0.1062, in 9 steps of 0.00158\n", "From time 0.1062 to 0.1205, in 6 steps of 0.00237\n", "From time 0.1205 to 0.2237, in 29 steps of 0.00356\n", "From time 0.2237 to 0.3999, in 33 steps of 0.00534\n", "From time 0.3999 to 0.6402, in 30 steps of 0.00801\n", "From time 0.6402 to 0.9525, in 26 steps of 0.012\n", "From time 0.9525 to 1.349, in 22 steps of 0.018\n", "From time 1.349 to 1.998, in 24 steps of 0.027\n", "From time 1.998 to 3.66, in 41 steps of 0.0405\n", "From time 3.66 to 4.876, in 20 steps of 0.0608\n", "From time 4.876 to 5.971, in 12 steps of 0.0912\n", "From time 5.971 to 6.929, in 7 steps of 0.137\n", "From time 6.929 to 7.134, in 1 step of 0.205\n", "(454 steps total)\n" ] } ], "source": [ "dynamics.explain_time_advance()" ] }, { "cell_type": "code", "execution_count": 25, "id": "8fe4bbce-f10b-4590-9cbd-97998745fc27", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABScaption
00.00000050.0000000.0000000.000000Initial state
10.00125047.9375001.8750000.1875001st reaction step
20.00250045.9718203.6609380.367242
30.00281245.5034684.0862030.410329
40.00312545.0406114.5064130.452976
..................
4506.5185461.5389959.35682439.104182
4516.6553881.5263669.27276439.200870
4526.7922301.5145749.19437639.291050
4536.9290721.5036319.12121439.375155
4547.1343341.4879839.01916839.492848last reaction step
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" ], "text/plain": [ " SYSTEM TIME A B S caption\n", "0 0.000000 50.000000 0.000000 0.000000 Initial state\n", "1 0.001250 47.937500 1.875000 0.187500 1st reaction step\n", "2 0.002500 45.971820 3.660938 0.367242 \n", "3 0.002812 45.503468 4.086203 0.410329 \n", "4 0.003125 45.040611 4.506413 0.452976 \n", ".. ... ... ... ... ...\n", "450 6.518546 1.538995 9.356824 39.104182 \n", "451 6.655388 1.526366 9.272764 39.200870 \n", "452 6.792230 1.514574 9.194376 39.291050 \n", "453 6.929072 1.503631 9.121214 39.375155 \n", "454 7.134334 1.487983 9.019168 39.492848 last reaction step\n", "\n", "[455 rows x 5 columns]" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history()" ] }, { "cell_type": "markdown", "id": "4f451620-86fd-4e3c-a060-6b506f78c13d", "metadata": {}, "source": [ "### Check the final equilibrium" ] }, { "cell_type": "code", "execution_count": 26, "id": "96424a3f-31da-46bf-81c0-0a85b9bc476d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: A <-> B\n", "Final concentrations: [A] = 1.488 ; [B] = 9.019\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 6.06134\n", " Formula used: [B] / [A]\n", "2. Ratio of forward/reverse reaction rates: 6.0\n", "Discrepancy between the two values: 1.022 %\n", "Reaction IS in equilibrium (within 12% tolerance)\n", "\n", "1: A <-> S\n", "Final concentrations: [A] = 1.488 ; [S] = 39.49\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 26.5412\n", " Formula used: [S] / [A]\n", "2. Ratio of forward/reverse reaction rates: 30.0\n", "Discrepancy between the two values: 11.53 %\n", "Reaction IS in equilibrium (within 12% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that all the reactions have reached equilibrium\n", "dynamics.is_in_equilibrium(tolerance=12)" ] }, { "cell_type": "markdown", "id": "fbeba7fe-7a4d-4223-aaa1-6b5b9b3cc1b8", "metadata": {}, "source": [ "#### Please note the much-longer timescale from the earlier plots\n", "If we look at early time interval, this is what it looks like:" ] }, { "cell_type": "code", "execution_count": 27, "id": "f8c50006-8c5d-405f-9442-7fd9e5d1274d", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=A
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", "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = px.line(data_frame=dynamics.get_history().loc[:250], x=\"SYSTEM TIME\", y=[\"A\", \"B\", \"S\"], \n", " title=\"Same plot as above, both only showing initial detail\",\n", " color_discrete_sequence = [\"blue\", \"green\", \"red\"],\n", " labels={\"value\":\"concentration\", \"variable\":\"Chemical\"})\n", "fig.show()" ] }, { "cell_type": "code", "execution_count": 28, "id": "5c44014b-9dee-4d8c-a2de-13478ee7bb63", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Min abs distance found at data row: 71\n" ] }, { "data": { "text/plain": [ "(0.02405919499545674, 23.73396682504195)" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Look at where the curves intersect\n", "dynamics.curve_intersection(\"A\", \"B\", t_start=0, t_end=0.1)" ] }, { "cell_type": "code", "execution_count": 29, "id": "ac0382c7-5940-4db7-b1df-80edd29c3336", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Min abs distance found at data row: 216\n" ] }, { "data": { "text/plain": [ "(0.14412951669101942, 6.026379520544665)" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.curve_intersection(\"A\", \"S\", t_start=0.1, t_end=0.2)" ] }, { "cell_type": "code", "execution_count": null, "id": "d70f2d6b", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 5 }